DAany shall run to and fro^ and knowledge shall he increased 



THE WORLD MACHINE 

THE FIRST PHASE 

THE COSMIC MECHANISM 



IN PREPARATION 

THE MECHANISM OF LIFE 
THE SOCIAL MECHANISM 



THE 

WORLD MACHINE 

THE FIRST PHASE 

THE COSMIC MECHANISM 



BY 

CARL SNYDER 



''Vicisti, Galileo!'' 



SECOND IMPRESSION 



LONGMANS, GREEN, AND CO. 

39 PATERNOSTER ROW, LONDON 

NEW YORK, BOMBAY, AND CALCUTTA 
1907 

All rights reserved 






'^V'^' 






TO 

THE ALL BUT FORGOTTEN MEMORY 
OF 

DEMOCRITUS OF ABDERA 

{ca. 460-360 B.C.) 

Justly esteemed by Bacon as the weightiest of the ancients ; 

Forerunner by a century of Aristotle and Euclid ; 

Geometer and traveller, physiologist and polyhistor, path-hewer and sage. 

He wrote illuminatively upon almost every branch of natural knowledge, 
in an Attic praised by Cicero as rivalling Plato's ; 

Founder of the Atomic Theory, and first of whom we know, historically 
to conceive this world and all it contains as a mechanism. 

To his ideas, 2000 years of invention, discovery, and research have added 
much but changed little. 



When now I had for a long time reflected upon 
the uncertainty that pervaded all the mathematical 
results then existing as to the motions of the planets, 
it began to be repellent to me that the philosophers 
who would investigate with such extraordinary care 
the most insignificant details of the course of the 
heavenly bodies, should yet find no certain ground for 
the movement of the World Machine. 

CopPERNicus, De Revolutionibus : Introd. (1543). 



Since Coppernicus, Man seems as if thrown upon 
an inclined plane, down which he is rolling, rolling, 
faster and ever faster — away from his central place 
in creation — Whither ? Into Nothingness ? Into a 
deep-penetrating sense of nothingness ? 

Friedrich Nietzsche, 

ZuY Genealogie der Moral. 



CONTENTS 

CHAPTER I 

IMAGO MUNDI 

PAGE 

The vv-orld-old effort of the race to construct a world image, a 
picture of the universe — Its history — It is scattered through a 
variety of works, most of which had appeared before the idea 
of evolution had taken hold — The permanence of our present- 
day conceptions ....... i 

CHAPTER n 

THE OVERCOMING OF APPEARANCES 

The whole intellectual and scientific advance has been characterised 
by the overturning of primitive impressions and beliefs — A 
survey of the wondrous change in our ideas which this process 
has WTOught — The implication . . . . .19 

CHAPTER III 

MICRO-MAN : THE BACILLUS ON THE WHEEL 

Endeavouring to portray the extraordinary difficulties with which 
man has had to contend in his struggle for knowledge — His 
helplessness and his ignorance — His littleness compared with 
the cosmos he has learned to know . . . - ^7 

CHAPTER IV 

THE BEGINNINGS OF CERTITUDE 

Primitive man and his world — His earhest ideas of fixity and law 
must have come from the development of mathematics and its 
applications — How he first learned " to count, to measure, to 
time, and to weigh " . . . . . .47 



X CONTENTS 

CHAPTER V 

BION AND THE DOCTRINE OF A ROUND EARTH 

PAGE 

The earliest recorded geometrical demonstration of the earth's shape 

— How he proved it — The mechanism of night and day . .61 

CHAPTER VI 

ERATOSTHENES AND THE EARLIEST MEASURES OF 
THE EARTH 

The earliest accurate measure of the circumference of the earth in 
Alexandria, B.C. 275 — The simplicity of his method — Subse- 
quent confirmation . . . . . • 7i 



CHAPTER Vn 

ARISTARCHUS AND THE DISTANCE AND GRANDEUR 

OF THE SUN 

The simple method by which he calculated that the sun was 300 
times the volume of the earth — Other calculations of the 
ancients — The littleness of the earth was early recognised . 83 



CHAPTER Vni 

THE TURNING OF THE EARTH : THE FIXITY OF THE SKY 

The teachings of Pythagoras, Philolaus, and others, as to the motion 

of the earth on its axis — Their mode of proof . . '97 

CHAPTER IX 

THE FLYING EARTH : THE FIXITY OF THE SUN 

The Coppernican system 2000 years before Coppernicus — It is in 
reality the system of Aristarchus of Alexandria — How he 
reached it — Why it failed of acceptance . . .109 



CONTENTS xi 

CHAPTER X 

ARCHIMEDES AND THE FIRST IDEAS OF GF^VITATION 

PAGE 

The ancients just failed of attaining to Ne\\i:on's discovery — The 

conditions which hindered them . . . .119 



CHAPTER XI 

DEMOCRITUS AND THE CONCEPT OF AN ATOMIC UNIVERSE 

His mode of reasoning — The grandeur of his conceptions — In their 

larger outlines the}' have been but little modified since . .129 



CHAPTER XII 

THE LEGACY OF THE GREEKS : THE REBIRTH OF TIME 

The ideas of Lucretius, Cicero, Cleomedes — It was aU a heritage 
from Greek science — The utter intellectual aridity of Roman 
culture — The submergence of Hellenic civilisation — Greek tradi- 
tions kept ahve by the Arabs — Their original contributions were 
slight — The cause of the Renaissance — The discovery of America 143 



CHAPTER XIII 

COPPERNICUS; THE TRUE SYSTEM OF THE WORLD 

His work was thoroughly in the modern spirit ; it was inspired 
undoubtedly by the discovery of America — What there was in 
it that was new — Its confirmation due to chance . .161 



CHAPTER XIV 

BRUNO AND THE RECEPTION OF THE COPPERNICAN IDEAS 

Bruno was the first to spread the Coppernican doctrine over Europe 

— His grandiose extensions of the doctrine — His tragic death 173 



xii CONTENTS 

CHAPTER XV 

KEPLER : PIONEER OF THE MODERN IDEAS OF 

NATURAL LAW 



PAGE 



He was the first to undertake to reduce natural phenomena to 
mathematical formulae — He was the forerunner of Newton in 
the ideas of gravitation . . . . . .183 

CHAPTER XVI 

GALILEO AND THE OPTIC TUBE 

He was the true inventor of the telescope — His discoveries as con- 
trasted with the meagreness of his resources — His greatest work 
was his investigation of the laws of motion and his foundation 
of dynamics ....... I95 

CHAPTER XVn 

THE ADVANCE TOWARD A RATIONAL WORLD CONCEPTION 

Ideas and contributions of Bacon, Descartes, Gassendi, and Hobbes 
— Descartes was the first distinctly to picture the world as a 
mechanism . . . . . . ,211 

CHAPTER XVni 

THE TRUE GRANDEUR OF THE SUN 

The first accurate measures of the sun's distance and size by 
Domenico Cassini — The amazing change which had already 
come over European thought . . . . .225 

CHAPTER XIX 

THE DEVELOPMENT OF MECHANICS : THE 
FORERUNNERS OF NEWTON 

Rise of the great mathematical school of the seventeenth century 
— Doctrine of inertia — The discoveries of Torricelli — Many 
minds on the edge of the law of gravitation . . .237 



CONTENTS xiii 

CHAPTER XX 

NEWTON AND THE MOTOR FORCE OF THE 
WORLD MACHINE 

PAGE 

The precise nature of his discovery — Its history — Just what it 

meant . . . . . . . . 251 



CHAPTER XXI 

HALLEY AND THE MESSENGERS OF THE GODS 

The terror formerly inspired by the appearance of comets — Its 
powerful influence towards superstition — Computation of the 
first cometary orbit — The first prediction and its realisation . 267 



CHAPTER XXn 

ROEMER AND THE PROOF OF THE EARTH'S MOTION 

How he came to his discovery — Its general rejection — Confirmed by 

Bradley's discovery of aberration . . . .279 

CHAPTER XXni 

LAPLACE AND THE STABILITY OF THE SOLAR SYSTEM 

The work of Newton taken up by the French mathematicians — 
Laplace and Lagrange determine that the planets constitute a 
stable system . . . . . . .291 



CHAPTER XXIV 

FIXING THE BOUNDARIES OF OUR SOLAR WORLD 

The ancient ideas of the world enlarged by the discovery of Uranus 
and Neptune — The triumph of the theory of gravitation through 
the calculations of Adams and Leverrier . , . . 303 



xiv CONTENTS 

CHAPTER XXV 

HERSCHEL AND THE HELTER-SKELTER FLIGHT 
OF THE STARS 

PAGE 

He demonstrates stellar motion^ and with it the motion of the whole 
solar system — The grandeur of his ideas — The wonderful advance 
from the time of Galileo to the death of Herschel . -315 

CHAPTER XXVI 

THE MEASURE OF STELLAR SPACES 

The forst successful measures of stellar parallax — The final proof — 
It supplies the absolute proof of the Coppemican theory — The 
size of the stars — The grandeur of Canopus — It may be a 
million times our sun . . . . . .329 



CHAPTER XXVII 

THE SPECTROSCOPE AND THE STUFF OF COSMOS 

The proof that the material of the universe is all the same — Other 

revelations — A second method of deri\T.ng stellar motion , 343 

CHAPTER XXVIII 

OUR PLACE IN SPACE : THE PLURALITY OF WORLDS 

The endeavour to fix the number of the stars — The difficulty — 
Probability of thousands of worlds in parallel development to 
our own . . . . . . , .353 

CHAPTER XXIX 

THE ASTRONOMY OF THE INVISIBLE 

Discovery of dark suns — Probability that their number vastly 
exceeds that of luminous stars — Binar\^ or t%^dn suns — The 
spectroscope and steUar collisions .... 369 



CONTENTS XV 

CHAPTER XXX 

THE STRUCTURE OF THE UNIVERSE 

PAGE 

Lambert's vast reveries — The evidence for the grindstone theory — 
The question of a central sun — Probabihty that the structure of 
the universe corresponds more to the modern kinetic theory of 
gases — Analogies . . . . . . .383 



CHAPTER XXXI 

THE BIRTH AND DEATH OF WORLDS 

The increasing evidence for the nebular hypothesis — Ideas of Buffon, 
Kant, Laplace, and their successors — Evidence from the theory 
of solar heat — Evidence from photographs of the nebulae — They 
are sketches of worlds in the process of creation . . -399 



CHAPTER XXXn 

THE COSMIC EXCHANGE OF MATTER AND LIFE 

Worlds and systems are not isolated as was formerly supposed 
— The incessant exchange of matter and energy implies a 
more or less homogeneous universe — Possible means of a 
cosmic propagation of life — Ideas of Kelvin, Helmholtz, and 
Arrhenius ........ 427 



CHAPTER XXXni 

THE LAST RIDDLE 

The problem of gravitation and the force or forces which hold the 
universe together — Gravitation seems insufficient — The mystery 
of an apparently inexhaustible outpour of attractive energy 
— Speculations of Newton — Modern attempts at a solution . 443 



xvi CONTENTS 

CHAPTER XXXIV 

THE END OF THE MACHINE 

PAGE 

The apparently increasing aggregation of matter — Evidence for 
the Spencerian formula — The existence of vast bodies like 
Canopus, a million times or more the bulk of our sun, seems 
to indicate the final congregation of the material of cosmos into 
a single inert body — The doctrine of energy likewise presents 
the simile of a clock that is running down — Resume and con- 
clusions — This volume to be followed by another on the 
mechanism of life and of human society . . .457 

Bibliography. ....... 469 

Index ......... 471 



CHAPTER I 
IMAGO MUNDI 



a<^\ 



Critias, long since, I know 

(For Fate decreed it so), 
Long since the world hath set its heart to live ; 

Long since, with credulous zeal 
It turns life's mighty wheel, 

Still doth for labourers send 
Who stiU their labour give, 

And still expects an end. 

Yet, as the wheel flies round. 

With no ungrateful sound 
Do adverse voices fall on the world's ear. 

Deafen' d by his own stir 
The rugged labourer 

Caught not till then a sense 
So glowing and so near 

Of his omnipotence. 

Matthew Arnold, The World and the Quietist. 



For the purged ear apprehends 

Earth's import, not the eye late dazed : 
The Voice said, " Call my works thy friends ! 

At Nature dost thou shrink amazed ? " 

Browning. Asolando. 



THE WORLD MACHINE 



CHAPTER I 

IMAGO MUNDI 

(J tot) 
Some morning afield, when you seem peculiarly alive, a mind all 
open to the clamour of sensations, impressions, ideas, let your 
eye range the sky — it is taciturn ; the hills — they are cryptic ; 
the sea, if it be there — its murmuring voice is confused. Re- 
flect then a little on what could be our ideas of creation, what 
sort of a " world image " we could form, if we had found no 
supplements or aids to the primitive senses with which we are 
born, if we had no miracle-working lenses and prisms, no angle 
measures, no strange magnetic needles, no Euclid, no long line 
before us of explorers and discoverers to write that ample page 
of knowledge which the pressed types make now the universal 
heritage of the race. As it would be to us, so it was to men 
and minds like yours and mine, ten, twenty thousand years ago. 

In ten or twenty thousand years, we may imagine, the face 
of the earth has changed but little. The sky, the monotonous 
wash of the sea, the hills, the plains, the yellow wastes of the 
desert, must have looked very much to the cave-dwellers as 
they do to us. The human animal, too, has not varied greatly 
— his dress, his speech, his social relations, a little ; the main 
activities of his daily life, his pleasures, his moral and economic 
problems, the struggle for existence, the ceaseless round of birth 
and death, remain much the same. What has so wonderfully 
changed in these ten or twenty thousand years is the human 
mind and its outlook on the world. 

The transformation has been immense — how immense we 
have learned but recently, through the larger development of 
anthropology, to know. The earlier ideas of mankind were 
almost pure fancy. The earth rested serenely upon the back of 



4 THE WORLD MACHINE 

a turtle, and the sun with Chesterfieldian urbanity stood still at 
the voice of the prophet. The imagination was unfettered and 
untrained. The coming of the spring, the yield of the harvest, 
the fate of battles, were conceived as in control of the gods. In 
the storm there were demons, in the fields there were fairies, 
in the woods the hamadryads played. There were omens and 
signs ; the conditions of a chicken's entrails might forecast the 
destiny of empires. In the antique world there was a universal 
belief in the intervention of the preternatural in the affairs 
of men. 

Little by little these beliefs fell away. In apparent chaos 
was found an order, and instead of caprice a scheme of nature 
in some sense understandable and in some sense predictable. 

The change was slow, the path obscure and difficult. Pro- 
bably the hardest thing the human race has had put before it 
to learn was the idea of fixity and consequence ; the certitude 
that one event follows inevitably from another — the notion, as 
we say, of cause and effect ; in Hume's phrase, of invariable 
sequence ; what we have come in latter days to style the reign 
of law. 

Even now it has penetrated but a very little way. It is the 
keynote of every rational work now written ; it adorns the 
pages of amiable efforts at the conciliation of science and 
religion. The phrase has a sort of literary vogue. Yet, at each 
new extension of this idea of fixity and law into our daily lives 
and thoughts, the generality cries out, just as it did at the 
motion of the earth, at the law of gravitation, at the scheme of 
evolution, and all the rest. 

The emotional side of the race has not changed. Law and 
fixity it will recognise now, after a painful effort, in the march 
of the heavens, in the course of the seasons, in the succession of 
geological epochs, of genera and species ; even in a vague way, 
in human development. But find this same fixity and law 
in the rise and fall of nations, of human institutions, of human 
beliefs, its creeds, its political doctrines ; to find this in the 
present primacy of America and the decadence of Spain; to 
view history as a tableau of destiny ; our daily lives, down to 
the minutest detail of actions " good " or '* evil," of thoughts 
" noble " or " vile," as the necessary and unescapable conse- 
quence of our surroundings which were created for us, our 
characters and bodily constitutions which were given to us : 



IMAGO MUNDI 5 

to view the world so — no, we are as yet very far from that ; 
for all practical consequences, scarce nearer than the barbarians 
who trembled before the thunder and offered human sacrifices 
to calm an infuriate Being above. 

It seems a formidable theorem to grasp. It might be called 
the pons asinorum of intellectual development, alike of the 
individual and of the race. 

But, if yet far from spiritual clarity, we have come some 
way. We no longer think the earth is fiat, as was probably 
true, for example, of Socrates or of Solomon. We no longer 
believe that the sun is a god ; nor do we regard it as an object 
two feet in width, as Epicurus taught. Nowadays frogs are 
not bom from the mud, as Aristotle believed. The alchemist 
who offers us a receipt for transmuting base metal into noble 
gold we receive with a benevolent smile ; the man with a new 
scheme for perpetual motion we know to be a crook or a fool ; 
and if a priestess of spooks may still befuddle many seeming 
sane and clever men, at least presidents and premiers no longer 
consult an oracle before they go to war. How has all this come 
about ? 

In a way we may answer : Through the growth of calcula- 
tion and experiment, and the invention of mechanical devices 
which have almost infinitely widened, corrected, and supple- 
mented our primitive five senses ; in a larger way, we may 
say: From an inherent impulse to know — the effort of^ "the 
restless cause-seeking animal " to probe the eternal riddle that 
surrounds and envelops him. Born into a world the mystery 
of whose phenomena fascinates even as it baffles, he has sought, 
undaimted by failure, undismayed by time, to find the elusive 
thread which binds events. It is the working of that instinct, 
not wholly absent in animals, which Renan calls the noblest 
craving of our nature : curiosity. It is the instinct of the 
child, whose incessant question is " Why ? — Why ? " It is the 
interrogation which must have troubled the childhood of the 
world: " What am I ? " " Where am I ? '' " Whence ? and 
O heavens, whither ? " 

From the infancy of the race there have been minds which, 
turning aside from the ordinary pursuits and passions of men, 
from the prizes of trade, from the clamour of war, from the 
pluckings of fame, have given over their lives to the search. 
Argonauts in quest of the golden fleece of knowledge and of 



6 THE WORLD MACHINE 

truth, their voyages have penetrated to the remotest corners 
of the earth and reached out among the stars. Magicians and 
sorcerers to tribal man ; philosophers, the lovers of wisdom, 
when Hellenism rose ; discoverers and men of science — Galileos, 
Newtons now — civilisation is their work ; the modern world 
is in some sense their creation. Amid the destruction and decay 
that attends all else from human hands, their achievements 
remain. The fabrics of the kingdoms melt away ; where Accad 
and where Carthage stood, no broken pillar Hfts its lonely form 
to mark the spot amid the desert silences. The dust and dreams 
of Caesar mingle with the forgotten ashes of his slaves. But 
Archimedes' lever and Thales' magic stone, the theorems of 
Euclid and Hipparchus' starry sphere, the magnetic compass 
of the dynasty of Tsin, and the black powder of Berthold 
Schwartz and his forerunners, the pendulum of Ibn-Junis and 
Hans Lippershey's far-reaching, near-drawing tubes, the presses 
of Gutenberg and Coster, the balance and retorts of Lavoisier, 
James Watt's labouring giants of steam, Volta's pile, and 
Faraday's whirling magnets, are possessions imperishable while 
civilisation, their fruit, survives. 

Thanks to five or ten thousand years, perhaps a still greater 
period, of tolerably connected and consecutive effort, there has 
been built up a considerable stock of knowledge which, deftly 
fitted together in an orderly way, has become our one sure 
guide in this weird journey through the wilderness. Supported 
by this slowly wrought fabric of fact and logical theory, it is 
possible now to give at least a partial answer to some of the 
primitive human problems. Relative to the rest of the cosmos, 
we know to some extent what we are, we know to some extent 
where we are, we have some slight idea as to whence we have 
come, we are beginning to perceive dimly whither we are going. 

Much of this is very new. In nature there is a certain 
tendency to the dramatic, some little also in the progress of 
knowledge. In some sense, it seems as if we had attained to a 
sort of climax. This may be but an illusion, born of the 
natural inability of the mind to see beyond its own day and 
time. It may be that the astonishing advance of the last 
three hundred years will continue without check, and perhaps 
with accelerated pace. Yet we know that such a dramatic 
moment came at the opening of the seventeenth century, with 
the establishment of our ideas of the solar system. So it may 



IMAGO MUNDI 7 

be that some future historian, chronicling the stages of human 
development, will write : — 

" It was at about the beginning of the twentieth century 
that man attained at last a true picture of the world — came 
to know, in brief, the cosmos as it is. It was at about this 
time that he came to perceive the eternal round of matter in 
the universe — the coalescence of vague and formless nebular 
masses into suns and satellites, their slow refrigeration into dark 
bodies, with the transient appearance of life, their dissipation 
again into primitive nebula through the incessant collisions to 
which they are subject. 

" It was then that he came definitely to conceive the whole 
scheme of world formation as a mechanical process, following 
simple and well-understood laws ; likewise that the incessant 
destruction of worlds is the result of a larger but still purely 
mechanical process. 

" It was at about the same time that he came to recognise 
that the germs of life are being driven each whither from one 
planet and one world system to another, under the pressure of 
light — that it is in this manner that sterile planets are fertilised ; 
that the varied life of these vast globes springs up under 
appropriate material conditions and in response to simple 
physical or chemical stimuli ; that the races of intelligent beings, 
v.4th all their attendant creations of civilisation, their art, 
literatures, sciences, institutions, are part and parcel of this 
same mechanical or physical process, and like the hills or the 
suns, like worlds or atoms, are the fleeting and mysterious 
manifestations of that eternal we-know-not-what, that under- 
Ijdng reality which is back of aU phenomena, whose nature it 
is not given to the conscious intelligence, part and product of 
it like the rest, to know. 

" In larger phrase, it was at this period that the more in- 
structed among men came definitively to regard the universe as 
a cyclic process — that is to say, as an unceasing machine, with 
no beginning and without an end. 

" This result came as the culmination of a period of un- 
paralleled intellectual activity, dating from the discovery of the 
New World and the appearance of a work by a Polish astronomer, 
wherein the true character of our immediate solar system was 
first adequately set forth. The accidental discovery of the 
telescope following shortly after placed in the hands of the 



8 THE WORLD MACHINE 

investigator an implement of extraordinary utility. In a few 
years the central force of the mechanism had been revealed by 
Newton. An immense development in the domains of physics 
and chemistry found a climax in the almost magical revelations 
of the spectroscope, which filled as it were the last gap in the 
circle of cosmic knowledge. So it was that in the brief space 
of three or four centuries, and after an incalculable period of 
blind groping, man was able at last to work out a rational theory 
of the world, complete in all its essential details." 

It may well be, let it be said again, that our present ideas 
of the cosmos, even in their larger outlines, are not yet final. 
They may be infinitely expanded with the years and the know- 
ledge to come. Yet in many considerable items of this know- 
ledge we may be certain that finality and completeness have 
been attained. Not so long as an intelligent ■ race of beings 
survives its precarious existence upon this globe shall we ever 
cease to believe that the earth is a ball eight thousand miles 
in diameter. We shall never cease to believe that it turns upon 
its own axis, or that it booms through an orbit about the sun. 
It is for ever inconceivable that we should ever change our 
belief that the sun is a million times the bulk of the earth and 
four hundred times further than the moon. It is inconceivable 
that any subsequent knowledge will ever change our ideas of 
the distance of the nearest visible stars. 

This much we know. 

In a way this makes up, for us, three-quarters or four-fifths of 
the cosmic landscape. It will abide. For when we speak of 
this knowledge as being so very new, at the utmost three 
hundred years old, in some sense we err. In some sense it is 
as old as the race itself. Our ideas of the earth upon which 
we dwell, of the orb of fire whose children, literally, we are — 
in a word, the whole world-picture, spacially at least, is the 
result of geometrical methods of reasoning and measurement. 
And geometry is old. It was old to the Greeks, who had it 
from the Egyptians, and we gather that the Egyptians had 
attained to a considerable stage of culture, intellectual and 
otherwise, certainly seven thousand years ago. 

And again, what is all our geometry and mathematics, what 
are all our inductions and deductions, our inferences and demon- 
strations, but the codified experience, not merely of the human 



IMAGO MUNDI 9 

race but of all conscious intelligence. A careful observer of 
nature's plan has very cleverly remarked that the deer, scenting 
danger in the wind, and gauging the direction, turns to flee 
oppositely, reasons no less scientifically, builds up the same 
complex inference from previous experience as does the man 
of science.^ The fox, eluding his pursuers by doubling upon his 
tracks, the hound in following the scent, and when it is lost 
beating about the bush in the expectation that it will be caught 
again, follows out a train of reasoning differing neither in degree 
nor kind, and probably but little less conscious, than Newton 
inferring the law of gravitation from the falling of the apple. 

With due deference to the piquant reveries of the geometers 
of multi- dimensional space, it is in little that we may con- 
ceive the main conclusions of Euclid vitiated through another 
two thousand or twenty thousand years. His axioms and his 
conclusions rest upon a registered racial experience — an experi- 
ence that, as Spencer was perhaps the first to point out, is now 
a part, an anatomical part, of the physical constitution of our 
minds. It seems a little lost to view that our ideas of space, 
our conceptions of three dimensions and no more, are the 
physical product of a physical process that began with the 
appearance of life upon the earth. If the fourth dimension 
existed, it would to-day be as distinctly a part of our current 
beliefs, as distinctly a factor of our modes of daily thought, as 
are the primal three. 

The foundations of science are firm. Its conclusions are not 
chimeras, unless indeed we are to accept the monstrous idea 
that the mind is so capable of turning round upon itself as to 
believe it has no individual existence. Like Kapila, in the 
early dawn of speculative philosophy, we may dream that 
" Neither I am, nor is aught mine, nor is there any I." It seems 
to the present writer there is no middle ground ; it is an 
absolute nihilism that must outdo the Fichtean akosmism as 
does the latter a Berkeleyan idealism, or the acceptance of the 
conclusions of experimental science for what they seem. 

For sane folk with a work to do in the world there will be 
little hesitation, and for them and all of those whose endeavour 
it is to follow in the pathways of the light, the horizons have of 
late been considerably enlarged. I doubt not that a future age 
will accord to our own something like a clear and somewhat 

1 Williams, History of Science, chap. i. 



10 THE WORLD MACHINE 

detailed conception of the cosmic Reality. In any event, 
whether this prove true or no, this surely is certain, that our 
present-day ideas of creation represent the highest flight, or 
in varied metaphor, the loftiest monument of the human mind 
which we possess. 

I wish to trace out the path and the method by which these 
ideas, these results, have been reached. Hereafter I shall 
present an argument, describe a doctrine, point out, as it were, 
the moral of the tale. But first of all there is need of a con- 
nected presentation of the facts. From age to age there have 
been various attempts towards such a complete world-picture. 
Their value naturally becomes impaired with the advance of 
knowledge. Such an idea was more or less the basis of the 
Hebraic Pentateuch, and indeed the fundament of almost aU 
religious systems has been an attempt towards an intelligible 
cosmogony. Such a work too, we may conjecture, was the 
Diakosmos of Democritus, written in the fourth century B.C., 
but now lost to us. A similar attempt is seen in Pliny's 
Natural History, in the first century a.d. ; in the works of 
Roger Bacon, the Admirable Doctor, in the thirteenth century ; 
in the Imago Mundi of Cardinal d'Ailly, which was the inspira- 
tion of Columbus ; in the Natural History of Buffon and in 
many another. 

In our own day the most noteworthy endeavour towards a 
complete physical description of cosmos was that made more 
than half a century ago by Humboldt. It was begun long after 
that splendid mind had passed the customary limits of pro- 
ductivity, before the doctrine of the conservation of energy had 
been established, and before it came to be understood that the 
sun is a cooling body whose light and life may one day die 
out — ^with it the light and life of the tiny bits of worlds which 
flutter in circles about him. In no later single work has 
Humboldt's vast design been realised. Such a work would be 
a summation, and more, of the physical sciences in their present 
state ; the task is probably beyond the powers of any single pen. 

The same is true of the historical side. The full story of 
the slow growth of this body of knowledge, of theory, and of 
ideas, is to be found only in pages the most diverse. It has 
been dealt with in a variety of works, rather drearily by Whewell, 
rather dreamily by Apelt, with a good deal of bias by Draper, 



IMAGO MUNDI n 

in graceful account by Williams, more technically by Bailly and 
Delambre, by Montucla and Libri ; various phases of it by count- 
less others. The volumes of Bailly comprise an exquisitely con- 
ceived work of high philosophic interest ; but it stops short even 
of Herschel and Laplace. There are some inspiring pages in 
Buckle, some instructive chapters in Lecky. But the work of 
Lecky begins in the Middle Ages, while the spirit of rationalism 
and inquiry, whose history he designed to trace, had flourished 
throughout Greater Greece through a longer period than in our 
modern world. The two volumes of Buckle are but a fragment, 
and in any event his work would have been a history of civilisa- 
tion in England only in the older and more restricted sense of 
the word ; it would have had nothing to do with the growth 
of English culture from its aboriginal elements. Draper treats 
of the intellectual development of Europe more as if it were 
the history of philosophies and religions and their political 
influence among one people and another. 

The history of materialism — that is to say, the endeavour 
to describe the world in terms of matter and force — has been 
very brilliantly set forth by Lange, from whom Tyndall drew 
the inspiration for his ever memorable Belfast Address. But 
the pages of Lange deal less with the acquisitions of positive 
knowledge than with the endless " systems " or poetical concepts 
of the philosophers. A valuable attempt to forefigure both 
the solid results and the speculative inferences of the last 
century is now in course of publication by Merz. Interesting 
memoirs and sketches of the more important protagonists of 
the great drama have been offered by various pens — to note 
but a few, of Aristotle by Lewes, of Newton by Brewster and 
Rosenberger, of the Alexandrian school by Matter, of the later 
conquests of astronomy by Bertrand, Lodge, and Gierke. The 
development of mechanics has been admirably portrayed by 
Mach, among others ; of physical theories by Duhem ; of 
cosmical theory by Wolf. The original contributions of von 
Helmholtz, Kelvin, and others, are to be found in their own 
works. There is a wealth of excellent monographs, dealing, 
either in detail or in a clear and popular way, with especial 
questions, from Sir Robert Ball, Simon Newcomb, Whetham, 
not to speak of many other volumes informing and valuable.^ 

The ramifications of the inquiry have to-day become so 
1 A bibliographical note will be found at the end of the volume. 



12 THE WORLD MACHINE 

vast that there is scarce any branch of physical science into 
which it has not reached, and from which it has not drawn 
facts of greater or less import in the make-up of the composite 
sketch. Of any recent volume dealing at once broadly and 
in detail with the materials for a cosmical theory, beyond doubt 
the most notable is the text- book of cosmical physics from the 
pen of Arrhenius. It may be that in this original and stimu- 
lative work we see for the first time in its entirety the cycle of 
the cosmic machine. 

In a larger sense we may now perceive that the development 
of a science of the earth and sun and stars, like human de- 
velopment in general, is an integral part of that vast scheme 
of evolution, of unfolding and becoming, which pervades the 
world. If life be universal, and of this we may little doubt, 
this growth of the race mind is a constant incident of the cosmic 
process. Doubtless in seons past other races upon infinitely 
distant planets have pursued the same difficult and devious 
way towards the light ; doubtless in aeons to come, when by 
the chance collision with some dark sun or huge swarm of 
meteorites our little earth and the system of which it is a part 
has been resolved again into chaos, the same process will be 
endlessly repeated within other systems possibly yet unborn. 

But for the here and now this development has been a 
human process, and in some sense forms the fairest possession 
of stumbling, groping humanity. It has been in especial the 
work of a small number of singularly gifted, intensely curious 
minds. Each of these facts had to be thought out, intently 
and sometimes painfully, by some particular brain or group. 
" Behind the fossil shell," says Taine, " there was an animal, 
and behind the library document there was a man." No part 
of our human growth is of profounder interest or of larger 
import for the future. 

In this it presents an inspiring contrast to the empty babble 
of wars and d5masties, of conquests and crusades, that passes 
ordinarily for history. The reading of the accustomed tales 
as a boyish pursuit is affected with an undivided charm. But 
he who in after years, when the boyish love of stirring tales of 
war and conquest and the pictured deeds of heroism has some- 
what passed, dips again into these predilections of his youth, 
turns the chequered pages with other feelings. Let him lose 



IMAGO MUNDI 13 

himself through an idle evening in a volume wherein the whole 
world-tale is spread ; his reverie, when the attention flags and 
the book is laid down, is one of mingled sadness and disgust ; 
of revolt at the spectacle of carnage and rapacity ; whole 
armies of men flung into a field to butcher each other for an 
envied province or an imagined slight ; arson and thievery, 
pillage and atrocious crimes applauded under the sounding 
name of conquest ; great cities sacked, the populations sold in 
degrading slavery, the women to shameful lives ; until a scant 
century ago, the lower classes lost in barbarism and ignorance, 
a prey to the wildest superstitions ; the upper class, a privi- 
leged few, despising work, despoiling the poor, licensed to 
pleasure, and often sunk in the grossest bestiality ; human 
beings tossed to lions to glut the savage lusts of a Nero ; heroes 
fed to slow fires for the preservation of the religion of God ; 
low intrigues and court scandal, and women parading their 
harlotry, because they are the prostitutes of an individual called 
king ; nations and peoples rising to the splendour of an Athens 
and then swept away ; mouldering stones where temples and 
palaces reared their graceful forms ; world capitals the haunts 
of jackals and the lizard blinking in the sun ; grandeur come to 
dust, and enterprises of great pith and moment all turned awry. 
A story of disillusionment, a theatre of riot and ruin ; a 
retrospect of what we commonly accept for history brings a 
weird and depressing feeling of its emptiness, its little importance, 
its pointlessness, its unworth. It summons the oppressed spirit 
of the melancholy Dane when he reflected on how 

" Imperious Caesar, dead and turned to clay, 
Might stop a hole to keep the wind away." 

Set over against this tale full of sound and fury is the 
steady advance of civilisation, often slow, often halted, but 
ever renewed ; the progress of invention, the amelioration of 
savage and brutal customs, the abolition of slavery, the wide 
diffusion of material comforts, of justice and of peace — in 
larger phrase, the broadening of the human mind, the heighten- 
ing of the human consciousness. Instead of the mood of 
Volney's Ruins, we have that of Macaulay's paean upon the 
Baconian philosophy ; instead of disheartenment, a buoyant 
and invigorating sense of things done, of progress and of 
attainment. 



14 THE WORLD MACHINE 

Look round upon the modern world, with its wealth, its 
broadened humanism, its beautiful cities, the ease of displace- 
ment, its universal culture, its patronage of science, the arts, 
the ennoblement of labour, and consider, then, that a few 
centuries ago our immediate forbears, the inhabitants of Great 
Britain and of the German forests, were painted and tattooed 
savages, who dwelt in huts of wattle and lived largejy by the 
chase. The Britons who met the invasion of Roman arms 
dyed their bodies with blue woad ; the Scots who resisted 
Agricola " fought naked and with short spears." Consider that 
so late as the Norman Conquest, in the eleventh century, the 
selling of men and women into slavery was a general custom 
in all parts of England. " You might have seen with sorrow 
long files of young people of both sexes and of the greatest 
beauty, bound with ropes and daily exposed for sale." So 
runs the word of a contemporary chronicler ; ^ and these were 
not captives of another race, not blacks nor prisoners of war, 
but " their nearest relatives and even their own children." 

Consider, again, that not its Parthenon, its Phidias, its Pericles, 
its serene and beautiful religion, could save the Athenian civilisa- 
tion from decay, which came doubtless through the ravages of 
disease, the exhaustion of the soil, and ineffective resistance to 
the inroads of the barbarian. Consider that the dominion of 
the Romans, and again of the Arabians, each insuring over 
wide areas the peaceful and pleasurable pursuit of life, were 
to be almost utterly swept away ; and reflect that our modern 
civilisation is secure. It fears no barbarian hordes ; it may 
fight disease. The plague will never again sweep away half 
the population of London. No fanatical sect will ever burn 
the library of the British Museum. The hundred universities 
of Europe and America, after a lapse of six or eight centuries, 
will not, we may believe, be the haunts of bats and owls as a 
hundred universities of the Saracens became. 

For all practical affairs, the theological, the ecclesiastical, the 
persecuting spirit, is all but dead; it will pass, and it will 
never return. In the political world there is a new order, an 
industrial order, and in the intellectual world there is a new 
method, the method of science. It is unbelievable that the 
mind of man will ever again spend itself for centuries over the 
arid and senseless disputes of scholasticism. It will not again 

1 Life of Bishop Wolstan, quoted by Taine, History of English Literature, 



IMAGO MUNDI 15 

gravely debate the number of the band of angels able to maintain 
its balance upon the needle's point. It will find scant leisure, 
we may imagine, for that barren and fruitless philosophy which 
in all ages has sought to penetrate the mystery of things by 
fixing its intent gaze, as it were, upon the navel of the mind. 

In the experimental investigation of the scheme of nature, 
the mind of man has a work to do ; but with the outer mystery 
it has nothing to do. We may conceive that in the times to 
come it will wholly give over the search for final causes or first 
causes, will recognise its vanity and its absurdity. What we 
call philosophy will be transformed or forgotten. After three 
or four thousand years man is no forwarder in his search for 
the meaning of things than when he began. Save in its content 
of positive knowledge, it is not clear that the philosophy of 
Spencer represents any considerable advance upon that of 
Democritus, who antedates him by twenty-three centuries. 
Alike they recognised the impercipience of the unknowable, 
which apparently the most of minds that betake themselves 
to metaphysics never can. The philosophers are like im- 
prisoned birds within a glass-house, beating their ineffectual 
wings against the panes, for ever drawn on by the illusion 
of apparent freedom and the seemingly illimitable expanse of 
attainable knowledge. For that matter the whole of the race 
is a good deal the same. 

But it is clear enough now that in some ways we shall never 
be any further advanced than we are. The simplest physical 
problem followed far enough, and usually it needs but a brief 
pursuit, lands the mind in the bogs of metaphysic. The 
ancient paradox as to the impossibility of contact between any 
two material bodies is but an instance among a multitude. 

It is with the same sense of impotence that we recoil from 
an endeavour to read any purpose or plan into the scheme of 
nature. The thoughts of men widen with the suns ; but " the 
increasing purpose " tends rather to disappear. The expansion 
of knowledge within the last few hundred years has been 
immense. Yet so far from bringing a real illumination of the 
larger problems of existence the mystery has been immeasurably 
deepened. 

Not upon Pisgah's heights nor in Patmian visions, nor among 
the fisher-folk of Galilee, we may imagine, has the riddle of 
the world been most deeply felt, but rather by Weimar's high- 



i6 THE WORLD MACHINE 

ways or in the garden at Down. When with open mind we 
regard the cosmos, ahke the infinitely little and the infinitely 
vast, there comes inevitably a sense of bewilderment and a per- 
plexity that seems hopeless. The universe seems in travail of 
some vast work whose purport or moral or object utterly 
escapes us. It is in vain that we seek for evidence of any 
purpose when we survey the heavens and contemplate the 
probability that therein is an endless welter of dead suns, per- 
haps hundreds or thousands of millions of them, incapable of 
bearing life, and so far as we may perceive, mindless and dumb. 
Their life is spent. Their sole use, so far as we may surmise, 
is simply to pursue an empty track through the wilds of space 
until, in a colossal catastrophe, they are dissipated again into 
the formless nebula from which they sprang, to become the 
spawn of newer worlds. 

It is in vain that we find any evidence of purpose or design 
in the appearance of the vast and uncouth lizards of the 
reptilian epoch — the gigantic brontosaurs that paddled about 
in the marshes, the fantastic pterodactyls who spread their 
darkening wings upon the heavy and mephitic air of that 
ancient time. Difficultly do we find a purpose in the tactics 
of a huge shoal of salmon entering a narrow pocket to destroy 
itself by the inrush of its own numbers. We fail to see the 
import or consequence that lies in the prodigious effort of the 
toiling millions of worker-ants that rear a million ant-hills, or 
of the mjnriads of coral polyps that weave the graceful atolls 
of the sea. 

It is equally in vain that we contemplate the scum upon a 
duck-pond. This scum is the product of life, is teeming with 
life. Yet the highest intelligence fails to discover for it the 
slightest utility ; and the instance is but one among thousands. 
It is with a perplexity bordering upon revolt that we consider 
the myriads of insects and of bacterial swarms which plague 
our human kind, breeding suffering and disease, and serving, 
so far as we may see, only to thwart the development of indi- 
viduals and hence of the race. If mere bulk or numbers were 
a measure of importance, in totality of bulk and numbers they 
must vastly outclass all the higher forms of life. 

We cannot recognise infinite goodness or intelligence in the 
avalanche, the cyclone, the lightning's bolt, the eruptions of 
Mont Pelee, the earthquake of Lisbon, the burning drouths 



IMAGO MUNDI 17 

of India, the famines of Ireland, the tidal-wave that flings up 
fifty thousand folk like so many drowned rats upon the coasts 
of Japan. We do not see the purport of an arrangement which 
covers the fertile lands of Europe and America with a sheet 
of ice once in a hundred thousand years or so, blotting out all 
life or banning it for an age. 

Not less vain is our endeavour to find in the cosmic order 
those qualities which we regard as the highest and noblest 
among men. Nature is not " wise," it is not " loving," it is 
not " economical," it is not " moral." It is flaunting in its 
unchastity, shameless in its impudicity ; its prodigality is not 
so much reckless as it is riotous. Its cruelty is savage, and 

" Red in tooth and claw, 
With ravine shrieks against his creed." 

Plundering and murdering at every step, it knows no justice. 
Fecund as an ale-wife, it abandons its children to every danger 
and to every ill, careless alike of those who survive or fall. 
Highly ingenious in some ways, its constructive intelligence is 
infinitely surpassed by its human progeny. King Alphonso of 
Castile was not the first to suggest that he would find no 
difficulty in devising a more perfect world than that in which 
he found himself. In the larger scheme as in the least, nature 
seems but a 

" Blind Cyclops, hurling stones of destiny 
And not in fury." 

The observation is banal ; in the pages of Stuart Mill and Spencer, 
of Renan, of Huxley, of Tennyson and Leconte de Lisle, of Mathilde 
Blind and Emily Pfeiffer, and many another, it has found ample 
expression. After them we may hope to have done with the 
frivolous and puerile phrases in which the attributes of creation 
were wont to be dressed. 

A religion of nature is a chimera, an antithesis of terms. 
The aims of Nature seem as various as its phenomena, and 
in the future the hallucinated mind which professes to surprise 
its secret will be regarded as the proper subject of the alienist. 

But if we may not explain, we may at least, in Schopen- 
hauerian phrase, describe. No untoward visit of some vagrant 
sun to our system interrupting, we shall in time complete the 
description of cosmos and of its contents ; but the " why " of 

B 



i8 THE WORLD MACHINE 

things will remain as obscure as now. So far as we can per- 
ceive, the evolution of worlds, of life and of societies, of art 
and the sciences, is a pervasive phenomenon of the universe, 
ceaselessly interrupted, incessantly destroyed, ceaselessly begun 
again, like the spider with its web, the beaver with its dam, 
the bee with its comb, man with his works. A little while ago 
it seemed as if we might perceive the obscure workings of a Con- 
structive Impulse in the scheme of the world. Its limitations 
eluding us, it seemed to promise much. But unless our present 
conceptions are radically changed, the idea of unending growth 
and expansion is an illusion, as if in entering a car of some 
gigantic Ferris wheel, and slowly lifted from the earth, we should 
believe that we should go on rising to the utmost reaches of 
the sky. The complement of evolution is devolution, and in 
the unfolding of worlds from a primal nebula, their slow decay 
and final resolution into nebula again, we can at present per- 
ceive but the ceaseless turning of a mighty wheel. 

From this primal nebula, this diffused chaos, this formless 
fire-mist, this aimless welter of the atoms, to the green and 
peaceful plains, where under a smiling sky the work of man 
is done, is a far cry. Not stranger nor more weird has been 
the intellectual journey of the race from its rude fancies, its 
fantastic imaginings, to its present godlike outlook on the 
universe. We may regard the one, like the other, as a process. 
Examined a little nearer, in what does this process consist ? 



CHAPTER II 

THE OVERCOMING OF APPEARANCES 



The lords of life, the lords of life, — 

I saw them pass, 
In their own guise, 

Like and Unlike, 
Portly and Grim, 

Use and Surprise, 
Surface and Dream, 

Succession swift, and spectral Wrong. 
Temperament without a tongue. 

And the inventor of the game 
Omnipresent without name ; — 

Some to see, some to be guessed, 
They marched from east to west : 

Little man, least of all. 
Among the legs of his guardians tall, 

Walked about with puzzled look : 
Him by the hand dear nature took ; 

Dearest nature, strong and kind. 
Whispered, *' Darling, never mind ! 

To-morrow they will wear another face, 
The founder thou ! these are thy race 1 " 

Emerson. 



CHAPTER II 

THE OVERCOMING OF APPEARANCES 

It was by an extraordinary mental effort that man came to 
know anything of the world wherein he lives. It was in the 
main a disillusionment, a struggle against and an overcoming 
of primitive impressions — that is to say, of appearances. There 
was, there is, little enough in his surroundings, in his daily 
life and experiences, to suggest to primitive man that the firm 
earth he treads is like the periphery of a wheel that is whirling 
him and all the things he looks upon — his habitations and his 
temples, the mountains and the seas — round and round with 
the velocity of a rifle bullet. No distance-posts flash by to tell 
him, or us, that between two beats of his pulse he has been 
shot through a space of 1500 feet, a quarter of a mile. The 
farthest stretch of level plain or even the boundless expanse 
of the ocean but dimly suggest, if at all, that his earth is round 
like a melon or a pumpkin. As we journey from Liverpool 
to New York we have no sense to make us realise that the 
engines below are driving 30,000 tons over a mountain 350 miles 
high, but with no more effort than as though the Atlantic were 
as level as a floor. 

If the earth be curved like a ball, are there, then, folk like 
us on the other side of it, straight beneath us, at the antipodes 
as we say — their feet to our feet, and hanging head downward ? 
And if there are, what is there to hinder them from dropping 
headlong into space ? So men reasoned once. And if this ball 
is revolving like the fly-wheel of an engine, at an incredible speed 
of 1000 miles an hour, 17 miles a minute, for any given point 
near the equator, how can anything be held to its surface ; why 
do not we and the oxen of the field, and all other things, go 
flying off at a tangent ? How does the atmosphere stay on ; 
why are the clouds not brushed away ? 

Again, as the thoughtful shepherds of Minor Asia, guarding 
their flocks, looked up into the sky, what could tell them that 



22 THE WORLD MACHINE 

the glowing ball which made their day was three-score million 
times the bulk of the silver disk which companioned their 
nights, and four hundred times as far away ? To the eye their 
diameters are equal ; looked at between thumb and forefinger, 
held at arm's length, or through a pair of sights set on a board, 
the angle they subtend is the same. There is nothing to make 
one think they are so very large, save perchance that they at 
times seem a good way back of the highest clouds, which in 
turn may lie far back of towering mountain- tops. Objects at 
that distance are often larger than they seem ; so Anaxagoras, 
friend of Pericles, Socrates, Euripides, conjectured that the sun 
is a body of red-hot iron, and may be as large as the whole of 
the Peloponnesus — that is, half as large as Greece. 

But it is a puzzle — to these ancient eyes — how these bodies 
get back again, after setting in the west, to rise once more with 
the dawn. They must have got round or under in some way ; 
it is very hard to say. Sometimes they are quite blotted out ; 
probably the gods are angry or evil spirits are at work, so the 
multitude will go out from the city and drum valiantly and 
shout, and drive the spirits away. But when the sun or moon 
appear again are they the same, or have the gods made new ones ? 
Even so wise a man as Lucretius, living in the same city beside 
Csesar and Cicero, is indifferent to which you answer make, if 
only you leave out the gods and put in their stead Nature, 
the fecund mother of all, who should be quite equal to the 
facture of a new luminary once in a while. 

By-and-by, when the shadow cast on the moon by the earth, 
the slow sinking of the ships below the horizon, the changing 
elevation of the pole-star as the traveller goes northward or 
southward, and the arching vault of the heavens have suggested 
the sphericity of the earth, it seems plausible to suppose that 
the sun revolves about it, and thus makes night and day. 

Aristarchus of Alexandria, pondering and measuring, con- 
cludes, eighteen centuries in advance of Coppernicus, that the 
opposite is true, that the earth sweeps round the sun. But 
who will believe it, who can imagine it now ? This solid earth, 
so vast that its curve cannot be measured by the eye, swung 
free in space, resting on nothing, and booming through the void 
at the speed of a million and a half miles a day, who can think 
it ? That is, 66,000 miles an hour, or from Land's End to the 
Orkneys while the second hand of a watch turns once. A 



THE OVERCOMING OF APPEARANCES 23 

modern 16-inch gun hurls a projectile weighing a ton, with a 
muzzle velocity of 2000 feet per second ; yet so swift is its 
flight that in its transit even this great mass is invisible to an 
observer standing by. The earth, could it be weighed at its 
own surface, would equal somewhat more than six thousand 
million billions (6,000,000,000,000,000,000,000) of these ton pro- 
jectiles, and it flashes through space at the rate of 100,000 feet, 
or 19 miles per second. An express train at 70 miles an hour 
does about 100 feet per second. 

If there were but stations along this circular railway round 
the sun — such, say, as the ancients imagined in the twelve 
signs of the zodiac — and we could take our stand upon a plat- 
form, we should see this solitary occupant of the track pass in 
40 seconds ; yet its greatest diameter would represent a train 
8000 miles long. In a day its huge bulk would have dwindled 
to the size of the moon ; in a week it would have disappeared 
among the trackless stars. And it would not return for a 
year. 

This strange, lone voyager of space, this planet, whirling so 
violently upon its own axis and plunging through the sky like 
a meteor, nothing above it, nothing below, runs its round of 
the sun all as if it were fixed to a track, or were skimming the 
surface of a sea. Yet as there is no track, no surface whereon 
to run, a looker-on might think of the earth as fixed to the end 
of an invisible arm 93,000,000 miles long, or held in leash like a 
stone in a sling. 

Some such fanciful mechanism is just what has been imagined 
and named Gravitation. Once it signified nothing more than 
the primitive impression of heaviness ; it was thought of, in 
Aristotle's time, as something real, just as was its opposite, 
Levitation, the tendency to lightness. It is not difficult to 
measure its effect, the force of its pull, and we know, since old 
Sir Isaac's day, the simple formula which describes its action. 
But when we try to conceive how across a hundred million miles 
of seeming empty space it can hold a colossal body like the 
earth to a rigid path, throughout long ranges of cosmic time, 
we are baffled still. It is a world riddle. 

Seventy times round the track and the little whirl of life is 
done. Of the first five one can remember nothing at all ; the 
next fifteen or twenty are passed in getting accustomed to one's 



24 THE WORLD MACHINE 

surroundings ; in the last ten the burden of the journey has 
begun to be felt. Of the forty remaining, one-third a man 
passes in an unconscious state he calls sleep. Finding his food 
and eating it, begetting, reproducing his kind, and hurrying 
about here and there like the restless ant, consumes the greater 
part of what is left. Scant wonder if, thus hobbled by the 
brevity of life, he should advance so little from one generation 
to the next, or that he should dream of another existence un- 
ruffled by the urgency of time. 

Seventy times round the track, but the great world runs on 
— how long ? Has it always been whirling along that self- 
same groove at the selfsame speed ? When did it begin — will 
it ever end ? Bodies so large, traversing intervals of space 
so fathomless, require obviously for their formation, for their 
disintegration, corresponding intervals of time, not thousands 
or millions but rather thousands of millions of years. The fly- 
wheel of a very ordinary engine will do a thousand revolutions 
per minute ; it makes its seventy turns in a few seconds, and 
a good engine may last for years. Whirling around a million 
or two million times a day, it is easy to see that the number 
of revolutions it will accomplish in its lifetime mounts into the 
billions. 

There seems no reason to believe that our heliocentric engine 
is less stable. It has no valves to clog, no j ournals to wear ; 
apparently space offers no resistance to its flight. It is noise- 
less, it seems to need no oiling, no care — no engineer. When 
was it built ? 

So long as the world seemed not so very big, our earth its 
centre and its grandest thing the sun, the stars revolving round 
it in some sort of way ; the simplest explanation of how they 
all came to be was that they were conjured into existence from 
the void by an arch-magician, as a spectacle for the gods. And 
unbiassed by disturbing considerations, it was not deemed pre- 
sumptuous to assign a date when the performance began. Thus 
Archbishop Usher ; the good man lived in the brilliant days of 
Shakespeare and Bacon ; he was fabulously learned in an age 
of scholars, and spent from the twentieth to the thirty-eighth 
year of his life reading the entire literature of ecclesiastical 
antiquity. Somewhat to the neglect of his slightly elder con- 
temporaries, Galileo and Kepler, he succeeded in fixing the 
creation of the world in the first week of January, 4004 B.C. 



THE OVERCOMING OF APPEARANCES 25 

The date may still be found on the margins of practically every 
Bible printed in the English language. 

The recent excavations of the tombs of the Nile kings, and 
of the great cities of the Syrian plains, reveal a people at a 
high stage of civilisation five and perhaps seven or ten thousand 
years before our era. Their temples, their palaces, their 
libraries, their sculpture, their jewellery, their sanitary and 
plumbing arrangements even, tell that even this remote day 
must have been but as yesterday compared with the distant 
time when troglodyte man left his bones, his weapons and instru- 
ments of flint, by the side of the remains of animals now in 
part extinct, in the caves wherein he dwelt. 

And this Stone Age is but at the surface of the series of 
superimposed strata of stone which must have required for 
their deposition, and alternate elevation and depression above 
and below the level of the sea, uncounted aeons. 

Yet again, it was hard to imagine that before the age of man 
strange races of animals prowled the earth — ^vast and uncouth 
saurians and pterodactyls, which would dwarf even the mam- 
moth ; how much harder to think that more than half of 
Europe and North America were once covered with ice ; to 
believe that Broadway and the crowded Strand, Himalayan and 
Cordilleran summits even, were once the floor of the ocean. 
It was long before there were any so to believe. Yet such is 
the unescapable testimony of the rocks, whose weird and ancient 
rime has never been more felicitously retold than in the haunt- 
ing lines of Tennyson : — 

" There rolls the deep where grew the tree. 
O earth, what changes thou hast seen ! 
There where the long street roars has been 
The stillness of the central sea. 

The hills are shadows and they flow 

From form to form, and nothing stands ; 
They melt like mists, the solid lands. 

Like clouds they shape themselves, and go." 

Projected into this '* dark Backward and abysm of time," 
the mind soars in a chilling and lonesome grandeur, and fain 
would go back to the lost gardens of Elysium, amid whose en- 
chanted spaces its childhood was spent. But the gates of 
toyland once passed are closed for ever ; and in the intellectual 



26 THE WORLD MACHINE 

life of the world it is the same. What the revelations of the 
telescope had implied, the advance of geognosy, of earth-know- 
ledge, has confirmed ; and to the conception of a universe 
immeasurably vast, we add at length that of an earth im- 
measurably old. 

But if the calculations of the good Archbishop slightly erred, 
still did it never have a beginning at all ? By an instinct born 
of familiar associations the mind refuses to accept such a con- 
clusion, and stirred by its restless fancy, will voyage where 
charts fail. It was from inquiry in another field that a clue 
came. 

If the earth is a ball and we live at the surface, what is 
inside the drum ? Is it hollow, and at the poles are there 
openings to an interior world — a fascinating world, perhaps, of 
gnomes and genii and dragons and elves and all the wonderful 
menagerie that was banished from the world of men ? The 
fire-spouting cones of the volcanoes scattered here and there 
over the earth suggest that it might be rather too warm. The 
eruptions of ^tna and Vesuvius, Krakatoa and Mont Pelee, 
seem to indicate that the inside is filled with molten rock. This 
appears to be confirmed when men mine into the ground and 
find the temperature increases as they go deeper and deeper. 

We live, then, on a crust that spans a glowing lake of fire, 
and on a crust that is very thin. If we took a sheet of paper 
and pasted it over the surface of a good-sized melon, we should 
have the relative proportions. 

AU this is strangely different from the early ideas of the 
race. This crust must have been formed by the cooling of this 
fiery mass. In cooling the mass would shrink. The earth 
may have once been a far larger body than now. Reasoning 
from the known effects of radiation and of attraction, we 
prolong the vision backward and see in a diffused fire-mist the 
beginning of the world ! A time was, perhaps, when the earth 
was part of the sun, when the sun indeed stretched out beyond 
the present confines of the solar system. Through the ages 
it has been shrinking, throwing off planets by times, and by its 
shrinkage flooding the world with warmth and light. So in its 
turn the earth parted with the moon, and in that cold and 
lifeless orb we have a presentment of what must one day be 
the fate of our globe as weU. 



THE OVERCOMING OF APPEARANCES 27 

Such is the grandiose perspective spread before our view. 
We may not greatly wonder that when it came to the mind of 
him who imagined it first, Immanuel Kant, he should exclaim, 
in an intoxication of the imagination such as possessed Archi- 
medes of old : — 

" Give me matter and I will build the world ! " 



If from out this fire-mist the earth, the moon, the sun have 
come, were these alone ? Holds space no others ? And if 
from chaos other worlds were born, where are they now ? 

When on the plains of Mesopotamia, or by the turbid 
current of the Nile, priests and herdsmen lifted their eyes to the 
firmament of stars, circling through the serene skj^ above them, 
and, as it were, striking the hours of the night, there was little 
enough to suggest to them that amid these points of light were 
other planets like unto our own. There is little enough now. 
But watching their course night after night as they wheel the 
heavens, the shepherds noted that there were some which failed 
to keep an even course. From night to night their pathway 
in the sky changed subtly. There seemed a place where these 
errant stars would pause and go back again. So they were 
named planets — the wanderers. Now and then the moon hid 
them from view. Now and then a dark spot was seen to march 
across the face of the sun. 

After a thousand years the course of these wanderers had 
been mapped. After a thousand vague conjectures, the idea 
began to grow up that they moved in circles, one behind the 
other, some between the moon and sun and some beyond. There 
came at last great organising minds like Aristarchus and 
Coppemicus to set these puzzling motions in order, to conceive 
this earth as a " wanderer " like the rest, and to picture them 
all as whirling round the sun. 

If from somewhere in the zenith of the system, and dowered 
with telescopic eyes, we might watch them, what a curious 
picture they would present ! — nine spheres, if we count the 
four hundred asteroids of " the shattered planet " as one, 
racing round and round ever so like the petites cheveaux of the 
spas and fairs with which Continental travellers are so familiar. 
Indeed we might conceive the huge Sirian of Voltaire's fanciful 
taJe, off on a vacation from his native dog-star, mistaking these 



28 THE WORLD MACHINE 

flashing, whirling planets for just such a machine, and, ignorant 
of Kepler's laws, backing little Mars for a winner against big 
Jupiter or the earth ! Surely a marvellous flight of the imagina- 
tion, thus to reduce the whole solar system to the workings of a 
wheel, not of chance but of fate ; and yet that is what the 
mighty intellect of Archimedes achieved. His planetarium, so 
admiringly and accurately described by Cicero,^ was mistaken 
only in placing the earth at the centre. Its construction was 
the feat of an intellectual giant whose mental level has been 
attained but rarely in the history of the race. 

Thirty times distant from the sun as the earth, and so faint 
among the crowd of stars that its character as a " wanderer " 
was not detected until sixty years ago, the planet Neptune 
lies at the outer rim of this solar wheel. The expanse of its 
orbit is unthinkably vast ; the earth, 90 millions of miles from 
the sun ; Neptune thirty times 90 millions. Already the earth 
has been lost in immensity ; viewed from the sun it would 
appear scarcely larger than does Mercury to us at its brightest, 
and far surpassed by Venus or Mars ; viewed from Neptune 
it would be invisible to the naked eye, as Neptune is to us. 

But the human mind, having reached such heights and 
depths, will not leave off. What lies beyond ? In what un- 
imaginable abyss of space is fixed the crystal sphere of the stars ? 
The objection urged by Tycho against the ideas of Coppernicus 
was that if the earth spins about the sun, the fixed stars would 
appear to occupy a different position according as they were 
viewed from one side of the sun or the other — say, at the 
spring and autumn equinoctials. There would be a certain 
displacement ; they would have an appreciable " parallax." 
And Tycho, observing genius as he was, could find none. 

But what Tycho, and GaHleo as weU, thus vainly sought 
has been found. Marvellous instruments, devised since their 
day, have detected the parallax of a considerable number of 
stars, and we know now that the distance of the farthest planet 
is to that of the nearest star as an hour to a year. The flight 
of light from the sun to Neptune, speeding at 186 thousands of 
miles per second, requires four hours, to the earth eight minutes, 
to the nearest star four and a half years. Try to comprehend 
it who can ! The moon is distant from us by ten circumferences 
1 De Republica, Book I. 



THE OVERCOMING OF APPEARANCES 29 

of the earth ; the sun is four hundred times the distance of the 
moon ; Neptune, thirty times the distance of the sun ; the 
nearest of the stars, nine thousand times the distance of 
Neptune. 

Viewed from the rim of the solar machine the sun has shrunk 
to a body no larger than Venus at its brightest. And outside 
this outer planet is a sphere 800,000 million times more vast 
than our whole solar system, within whose black and desert 
emptiness there swims no star, no sun, to light the soul upon 
its journey to a fairer world. 

Still undaunted, the mind of man, rising to horizons yet 
more vast, questions still : What lies beyond ? 

We may, if we like, picture the emptiness which lies outside 
our little solar world as a colossal hollow shell, enveloping it as 
one sphere may be made to fit over another. We may more 
than double the diameter of this shell, conceiving its outer 
surface at half again the distance of Alpha Centauri, and still, 
so far as present measures of parallax go. Alpha Centauri will 
be the only other occupant of the void. Light travelling at 
660,000 millions of miles per hour will be ten or twelve years in 
crossing such a space from one boundary to the opposite. It 
follows, therefore, that if we could suddenly materialise this 
shell, so as to cut off the light of all the stars of heaven, it would 
be at least three years and a half before we should become aware 
that it had been done. 

The number of the stars, we know, is as the sands upon the 
shores of the sea ; not, there is some reason to think, infinite, 
but perhaps even now, in a vague way, estimable. And if in 
truth their number be finite and knowable, so then is the uni- 
verse not boundless, but its extent and its shape may one day 
be known. We are here upon the edge of the future. 

Some tentative calculations have already been made, ex- 
quisite in their simplicity, confounding in their results. They 
are as yet new ; they will doubtless be revised. Not improbably 
there are stars a thousand times more distant than our nearest 
neighbour stars ; remote from us thirty thousand years of 
speeding light. The mind gropes in vain for units, mile-posts, 
to fathom such immensity of space. To vary a simile now 
grown a trifle antique, had these distant suns been extinguished 
in those remote and charming days when the moon paused in 



30 THE WORLD MACHINE 

its peristaltic way, to sojourn in the valley of Ajalon, and the 
sun, not then grown to its vast proportions, and more attentive 
to the admonitions of the prophets, rested for a space upon 
Gibeon, these stars would still be shining for us in the sky. 
Or, in another way, though in a crash of colliding systems, some 
mightier Sirius might have blazed out in the heavens thirty 
centuries ago, its light would not yet have reached this earth 
to tell us of the fact. 

A little dulled to wonder, the fabulous in science grow a 
little stale, these disclosures we read with the nonchalance that 
we skim the morning paper. They bring no stirring of the ancient 
awe. But when two centuries ago the curtain was first drawn 
aside, we shall not greatly wonder that the imaginative and 
trembling soul of a Pascal, before such a vision of the infinite, 
should recoil in fright. 

So with the conception of a plurality of worlds. It was hard 
to think of, once. In the solitude of the cloister a Bruno hears 
the message of Coppernicus, reflects, and flinging aside his 
monkish robe, shouts across Europe : " The stars are suns." 
For his crime the blazing faggots roast his quivering flesh. 
To-day it is a commonplace of astronomy, and with it the belief 
that round these suns swing myriads of planets like our own. 
And if life is merely a stage of planetary evolution, then we 
must conceive that in the desert distant ways there are count- 
less earths like unto our own, and undergoing the same strange, 
uncertain, fumbling, stumbling development of which this globe 
is the theatre. 

Shrinking suns, dead moons, and dying worlds — is cosmos 
a clock that is running down ? May we look forward to a day 
when, moons and meteors having fallen back into the planets 
which gave them birth, the planets in turn into the suns of 
which they were once a part ; the suns drawn inward into a 
central mass, coalesced with the billions of other suns ; the 
last star having shed its smokeless glow and gone out ; the 
last particle of matter quivered with the last vibration of heat ; 
the universe, a lifeless inert clod, sunk to the coldest cold of 
space, shall be at rest — at last ? Is such the prospect ? 

It may be ; there is no certainty. Spacing the starry ways 
we find here and there a formless luminescence, faintly glowing 
like a wisp of cloud that sometimes floats across a summer's 



THE OVERCOMING OF APPEARANCES 31 

afternoon. These are the nebulae, the fire-mists, from which 
new worlds are born — the spawn of cosmos ! Could we stand 
by, and time for us stand still awhile, then here within these 
primal wombs we might watch the slow gestation and parturi- 
tion of a race of Suns and Saturns, Nep tunes, Jupiters, Mars, 
and earths — perchance the next cosmic generation to our own. 

We reach here the astronomer's last word ; the Book of 
Revelation, for the moment, ends. But what visions it con- 
jures — what a distance from Chaldea we have come ! Weird 
welter of worlcfe and races and terms and times, could we con- 
ceive of some vast being to whom our globe would appear but 
a mote floating in the air, and seen only in the pathway of a 
sunbeam, what a curious spectacle the universe would offer to 
his view ! A chaotic, whirling, wildly dancing swarm of fire-flies 
the suns would seem, each glowing its little turn and dropping 
away, while another lights its lamp ; swarms and swarms and 
never an end ; no heaven above, no solid earth below, no foot- 
hold in infinitude. 

So in the world of thought the soul of man. Visions of 
science ? — 'tis a nightmare rather, like that vertigo of dreams 
wherein we seem falling through some vast abyss, and pale and 
trembling wake to find our horror but a figment of the mind. 
So we may wake. 

Led thus by slow and stumbling steps to the summit at 
last, whereon he looked out, as it were, upon a universe of un- 
ceasing motion, without apparent bounds in space or time, man 
could but feel as we feel still, a profound and depressing sense 
of his littleness, his nothingness. Yet may he still reflect, with 
Pascal, that it is he who sees, he who is conscious of the wonder, 
and not the wonder itself ; that the universe seems mindless, 
blind, and dumb ; in a way this world about him, so inimitably 
vast, is but the creation of his own senses. If he like, he may 
dream with good Bishop Berkeley that it is all a dream. 

Yet comforting as may be the legerdemain of an idealised 
idealism, there are still few among us who, whatever they may 
think regarding the problem of the external world, doubt that 
they themselves exist ; and it needs no long pursuit of the 
will-o'-the-wisps of the Ich and non-Ich to assure oneself that 
in the unguarded moment we assume that we ourselves have 
a personality and a being, we let in the whole procession of 
appearances which come of the six gates of the senses. The 



32 THE WORLD MACHINE 

nebular hypothesis, the Ught-bearing ether, the atomic theory, 
and all their like, may be but convenient " working hypotheses," 
but it is well to remember that, in the absence of negative proof, 
they stand on more or less the same footing as the hypothesis 
that a being you call you, O Indulgent Reader, scans these 
lines. 

The phantoms of Idealism were born in Greece ; and though 
many have embraced, they have proven as barren as the vestal 
virgins of final causes. Stimulated by the amazing results of 
his endeavour to learn something of the world about him, man 
sometime since turned from inquiries into the nature of being 
to an examination of the parts of which his own being was 
composed. 

If in his discovery of the revolutions of the earth he had 
bagged an engaging paradox, in his anatomical studies he cap- 
tured a troop. For he was not long in perceiving that the 
various parts of himself bore a singular resemblance to the 
implements and contrivances of his workaday life. Little by 
little he came to see that the heart is a pump and the blood- 
vessels an intricate system of irrigation. The lungs are bellows, 
worked automatically from a centre at the base of the brain. 
The muscles are pulleys and the bones are cranes. The eye is 
a telescope, the ear an inverted megaphone. The kidneys are 
filters, the liver is a sugar factory, the stomach a vat for fer- 
menting food, the thirty feet of coiled piping of the intestines 
the vital still where strength, warmth, courage, good feelings and 
bad, and all our outlook upon life are brewed. 

Even the process of reproduction he came to realise was 
much like planting corn in the field ; and if the growth of the 
corn was mysterious, hardly less so was the working of yeast 
in a lump of dough, or that a mixture of charcoal, nitre, and 
sulphur, properly pent up and set fire to, should throw a cannon- 
ball some miles. 

Moreover, the chemical ingredients making up this strange 
being, capable at once of the sublimity of astronomical dis- 
coveries, and of burning old women, maidens, and men for 
witches or heretics — sometimes so near a god, sometimes a 
ravening savage — ^were found to be simple in the extreme. 
Water is the most important by nine-tenths. We know how 
water, skilfully mixed with a little glue or gelatine, makes a 



THE OVERCOMING OF APPEARANCES 33 

viscous mass much like the shme of Hfe we call protoplasm. 
Add some charcoal from the hearth, some nitrogen and oxygen 
from the air, mix in a little sulphur, take some phosphorus for 
the brain, a trace of arsenic and some of the mineral salts, and 
the analysis, alike for a Shakespeare, a Newton, or a witch- 
burner, is complete. 

True, we may not as yet take carbon, water, ammonia, and 
a few salts and produce living matter ; but I think the day 
when we shall is less distant than the end of the world. 

If the telescope, reaching into the depths of stellar space, 
has seemed to reduce not merely man on his earth, but the 
whole solar realm to an atom of the cosmos, he has found in 
the microscope and in the test-tube of the chemist the salva- 
tion of his pride. But the revelations of the latter have not 
been less destructive to his primitive ways of thought. 

Thus as he has found the heavens stretching away in 
a seeming unending welter of suns, so, floating invisible in 
the air about him, in the very air he breathes, he has learned 
to know that there are organisms so minute that, compared 
to them, he is a greater figure than the earth to him. They 
may and do infest the body in multitudinous hordes, and he 
be never aware of the fact. These are living beings, for they 
grow and reproduce as do other living things, and yet their 
organisation is so relatively simple that already the chemist, 
entrenching upon the domain of the physiologist, has caught 
a glimpse of their physical structure. It was, in truth, from 
their action upon different substances, that Pasteur, a chemist, 
was led to their discovery. And just as to-day the organic 
chemist takes apart the molecules of one kind of sugar to put 
them together again in another way to form forty other kinds, 
so the amazing achievements of Emil Fischer and his fellow- 
workers point to the day when they will do the same with the 
molecules of living matter which make up a microscopic 
bacterium. 

Indeed, even if such a result had not been predicted by 
the recent attainments of biological chemistry, it would have 
been foreshadowed by the equally astonishing advance of his- 
tology, or micro- anatomy. It is a commonplace of these latter 
days that alike the oak and the turtle, man and all things living, 
are made up of bacteria-like units, the cells. By processes hardly 

C 



34 THE WORLD MACHINE 

less ingenious than those which have enabled the astronomer 
to divine and weigh dark suns, for ever invisible to the human 
eye, so the present-day anatomist, with his refined objectives 
and staining reagents, has penetrated the inner structure of 
the cell itself, watched it enveloping, digesting, and ejecting 
its food, joining in marriage with another, and then forming 
the beautiful astral figures, so suggestive of a magnetic field, 
which are preliminary to the birth of a new generation. 

Thus pressed, on the one side by the chemist, on the other 
by the anatomist, we attend as it were the approaching juncture 
of two armies, whose coalition will mean the explanation of 
life in terms of valencies and atoms. 

" In the beginning was chaos," the tutor of Epicurus ex- 
plained. " And where did chaos come from ? " the young man 
asked. Following out the previsions of Democritus, advancing 
knowledge has seen all existing things, the living and the life- 
less, the sentient and the inert, reduced to the invisible, and 
in the older view, indivisible atoms — " the foundation-stones 
of the universe." But what are the atoms ? What are these 
seventy odd elementary substances which can no longer be 
resolved ? Are they the " massy, hard, impenetrable particles " 
that Newton fancied, " even so very hard as never to wear or 
break in pieces ; no ordinary power being able to divide what 
God made one in the first creation " ? 

We must wait for the answer. We seem to hover on the 
brink of a new revelation, the explanation of matter itself — of 
matter and of the other great mystery, of electricity, as weU. 
A something smaller than the atom, the cathode " rays," the 
electron or ** corpuscle," seems to have been found. We live 
in days of wonder, still. 

Meanwhile, however the newest discoveries may turn, we 
know that in the spectra of the suns and stars the lines of many 
of our so-called elements do not appear. Conceivably in the 
fiercer heat of these blazing worlds some of the elements have 
been resolved ; perchance, somewhere, all. They may be the 
result of condensation and cooling from temperatures which 
man has not yet been able to attain. Perchance in the primal 
fire-mist there was but one, the urstoff, the protyl, of the cosmic 
mind. 

We here reach bounds. Further the mind cannot go. Or 



THE OVERCOMING OF APPEARANCES 35 

rather, starting thus in either direction, and covering in its 
stupendous flight the ineluctably vast, the inconceivably small, 
it gains at least a common goal. Here pausing, it endeavours 
to bind the retrospect in a single principle, to link macrocosm 
and microcosm in a single enveloping conception. Rising from 
the analogy of the growing tree or the unfolding petals of a 
flower to see a kindred process in the whole spectacle of nature, 
it sums the course of universal development in a word — 
Evolution. 

It is to be noted that we have here an analogy, a description, 
and not an explanation. It is expressly unconcerned with any 
thoughts of Cause. It was simply that with his ever-widening 
vistas of space and time man had found the more primitive 
simile of the potter and the clay had ceased to be adequate. 
Advancing knowledge had revealed a world awhirl — a whirling 
earth, a whirling sun,, whirling planets, whirling atoms, and 
whirling stars. If the idea of an intervening artificer was to 
be retained, it would needfully have been under the altered 
guise of a maker and spinner of tops ; and the notion seemed a 
little bizarre. So from the symbol of the architect the mind 
of man broadened to conceive the whole of nature as an 
organism, subject to universal laws of growth and decay. For 
the old anthropomorphising theognosy it substituted a process, 
an unfolding, a becoming. 

The idea of evolution, not less than the picturesque demons 
and deities of the antique world, was essentially a poetical 
conception — the effort of the mind toward a world-image. It 
seems to be a little lost to view that all world-pictures, all 
cosmogonies, are that, and no more than that. Herbert Spencer 
and Darwin, no less than the Pentateuchian theorisers and all 
their forerunners, were essentially poets, only dowered with a 
more highly developed imagination and a loftier range of thought 
than usually accompanies the merely rhyming brain. 

And again, the idea of evolution was a stage, a step higher, 
in the unfolding of the world mind. Advancing knowledge is 
building yet a higher stage, approaching a yet wider view. It 
was more especially with the phenomena of life, the unfolding 
of new species, new races, new institutions, that the idea of 
evolution was concerned ; and as the processes of life, growth, 
birth, and death are brought more and more within the domain 
of chemistry and physics, the evolutionary imagery must give 



36 THE WORLD MACHINE 

way to a generalisation more definite and more precise, and 
less a poetical simile than a statement of fact. 

With biology lifted to the rank of a physical science, and, 
in the phrase of Huxley, become a problem in molecular 
mechanics, we shall turn, I think, from the analogy of the 
flower and the tree to that of a world machine. 

A doctrine as old as philosophy itself, refurbished by 
Descartes, and though he himself did not see it, inexpugnably 
fortified by Newton and by his discoveries, the idea of the 
universe as a mechanism is as yet very far from prevalence 
among the minds of men. 

In the pages that follow I purpose to go back to the simplest 
beginnings of things — to the days when primitive man first 
learned to count, to measure, to time, and to weigh, and to 
mark out how his every step toward positive knowledge has 
been an advance toward mechanical conceptions of phenomena 
which must one day end in a mechanical conception of the whole. 
In a word, since strict logic has been of no avail to convince, 
I purpose to offer the induction of history, to endeavour to 
construct, as it were, the curve of the development of our know- 
ledge of this world, and by the logic of its continuity, bridge 
certain obvious gaps which as yet remain to be filled in. 

There are types of minds to which the idea of Necessity 
brings a vague shudder, as at the closing of iron gates. At each 
great step in the development of our world conceptions these 
emotional natures are stirred to revolt, or fright. But if the 
larger knowledge seems to subtract ahke from the individual 
and the race something of their old importance, we need not 
forget that this knowledge is ours, and has been dug out by the 
race itself. Perhaps this is the true wonder. In any event, 
let us not lose sight of the grandeur of the achievement ; for 
in it the intellect of man has in some sense turned round upon 
its antecedents and the universe of which it is corporeally 
so infinitely shght a part. 

The theme is epic ; but the bards are voiceless, the tale 
untold. We shall scarce lose ground if we consider for a 
moment what manner of being it was that could unclasp and 
read the book of the seven seals. 



CHAPTER III 

MICRO-MAN: THE BACILLUS ON THE WHEEL 



Und schnell und unbegreiflich schnelle 
Dreht sich umher der Erde Pracht ; 
Es wechselt Paradieseshelle 
Mit tiefer schauervoller Nacht ; 
Es schaumt das Meer in breiten Fliissen 
Am tiefen Grund der Felsen auf, 
Und Fels und Meer wird fortgerissen 
In ewig schnellem Spharenlauf. 

Faust. 



What peculiar privilege has this little agitation which we call 
thought that we must thus make it the model of the universe ? 

Hume, Dialogues Concerning Natural Religion. 



CHAPTER III 

MICRO-MAN: THE BACILLUS ON THE WHEEL 

Our human pride is great ; and the love of vain boasting does 
not end. Yet in one noble regard it has ofttimes seemed to the 
present writer that scant justice, scant appreciation, has been 
done to the deeds of our human kind. 

" Zwei Dingen erfiillen das Gemuth mit immer neuer und 
zunehmender Bewunderung," wrote the son of the saddler ; and 
Tyndall repeats after him in a memorable address. Yet the 
" two things " were not the same with Tyndall as with Kant. 
For the prophet of the Scientific Imagination they were neither 
" the starry heavens " nor the " moral sense of man," rather 
—the littleness of man, set over against the grandeur of the 
cosmos he has learned to know. But to how many of us has 
ever come any vivid realisation of the struggle and the odds ; 
man's extraordinary physical insignificance in the face of the 
world in which he lives, the seemingly insurmountable diffi- 
culties which have impeded his amazing explorations of the 
unimagined and unknown. 

The littleness of the earth as compared with the sun is a 
commonplace. Consider the littleness of the human biped as 
compared with the globe of the earth. The diameter of the 
sun is but one hundred and nine times that of the earth ; the 
diameter of the earth is not hundreds, or thousands, but millions 
of times the height of the tallest man. 

Consider what a pigmy he is compared with the bulk and 
height of a soaring mountain peak, and yet that the greatest 
of these in no wise disturb what to an extra-mundane observer 
would seem the exceeding smoothness and polish of the surface 
of this sphere. Alike peak and sphere micro-man has learned 
to explore, to measure, to weigh — moon, sun, and hidden stars 
as well. Yet the wonder of it all seems dead. No poets sing 
the majesty of the mind ; prattling apes chatter of " the 
bankruptcy of science " ; we learn as children the results of 

39 



40 THE WORLD MACHINE 

this long and wondrous march of the intellect, with no hint of 
the difficulty, no inspiring presentation of the struggle, no 
awakening to the splendour of the conquest. 

It is perhaps that we lack an adequate measure of the feat. 
But as the astronomer, unable like the surveyor to carry his 
chain to the moon, may yet calculate its distance from measures 
of its parallax, so perhaps by recourse to analogy, the parallax 
of the mind, we may find a help. 

Swift, in his classical tale, imagines a race of elfish men so 
small that hundreds of them may climb about over his body. 
Let us try to conceive of a race somewhat ten thousand times 
smaller — that is, a race which has the same relation in stature 
to us as the diameter of the earth to an average man. It 
chances that within the last forty years we have come to know 
that beings of these ultra-microscopic dimensions actually 
exist : the minute fungi which, for good and evil, play so over- 
shadowing a part in our daily lives — the bacteria. It is a 
somewhat curious fact that, with the perfection of oil-immer- 
sions, anastigmatics and their like, the eye is now able to 
perceive and study microbian races of just the proportion we 
seek. It would require about eight million men of average 
height, one standing on another's head, to equal a diameter of 
the earth. On the outermost fringe of visibility a modem 
microscope shows objects which stand in the same proportion 
to man. 

It is a little difficult to form a vivid mental presentation of 
just what this relationship means. The naked eye is puzzled 
to detect points set much closer than a hundred to the inch ; 
two or three hundred dots to the inch is for most eyes a con- 
tinuous line. This is about a fine hair's-breadth. The unit of 
microscopic measures is the micron, marked with the Greek 
letter [jl, and these run 25,000 to the inch. The lower hmits of 
visibility of present-day microscopes is from a quarter to a 
seventh of a micron. Doubtless there are living beings some- 
what smaller ; but a bacillus whose body is of these dimensions 
— that is, about the hundred thousandth part of an inch — is 
the smallest thing we know of alive, and it is the smallest thing 
that the human eye has ever seen. An average human being 
is very closely eight million times this in height. 

Bacilh are, as we are learning slowly to know, organisms of 
an unsuspected complexity. They vary too in size, in shape, 



MICRO-MAN 41 

in function and activity, almost as much, one might say, as 
our gross animal world. Among them, if we may give fancy 
a rein, we might imagine elephants and dogs, horses and 
hippopotami, and all sorts of others. And we now know that 
they are numbered like the leaves of the forest. The large 
intestine of a man, for example, contains, normally, a bacterial 
population perhaps a hundred thousand times the human 
population of the earth — say a hundred to one hundred and 
fifty billions. 

For the moment we will endow this microbe with a brain, 
though doubtless he possesses none ; such vague sensations as 
he has he experiences, probably, with his whole being. We 
will give him hands to grasp with, feet to travel on ; imagine 
him like a man, infinitely curious, but soon tired ; able to go 
but a very little way when he must lay his head against the 
earth and sleep. 

This being I will conceive in precisely the same habitat as 
that of man, as that of our own : I mean upon the fly-wheel 
of an engine — upon the surface of a very smooth and polished 
fly-wheel, turning at 4000 or 5000 revolutions per minute. It is 
little that we commonly think of our earth in such a guise ; but 
equally little that we ever think of ourselves as one eight- 
millionth part of the diameter of the earth. We are insensible 
to the prodigious spin of the globe ; equally so, let us say, is 
a bacillus upon a top. A wheel corresponding in size to this 
microbe as the earth to man would be of course about five or 
six feet in diameter ; but there is no fly-wheel as large as this 
which turns at such a speed. The fly-wheel of a motor-car — 
the most familiar example one may choose nowadays — makes 
from 500 to 1500 revolutions ; and it is quite impossible to see 
anything on its surface even at the slower speed. 

Whirling at such a velocity, the first thought of course 
is that this microbe would be instantly swept off the wheel. 
There is no need of alarm ; he is peacefully roaming about in 
the plains and the valleys that extend all over the wheel, for 
looked at under the microscope the surface of the wheel, polish 
it as highly as we may, is still mountainously " scarred and 
thunder-riven." 

And does any one conceive that the smooth surface of the 
fly-wheel does not answer to the rugged face of the earth ? 
Let him then compute our highest Alpine or Himalayan 



42 THE WORLD MACHINE 

rugosities ; he will find that, reduced to an object he may 
hold in his hand, the earth would be smoother than any billiard 
ball can be made. But the atmosphere, the air which this 
bacillus must have to breathe ? — for breathe like us he must. 
The layer of atmosphere in which man may exist bears the same 
relation to the earth as a thin sheet of paper would, pasted 
down upon such a wheel. Probably every fly-wheel carries on 
its surface a very thin layer of air roughly, though very much 
thinner, corresponding to the earth's atmosphere. 

What now might be the thoughts and sensations of this 
micro-man, this bacillus on the wheel ? What idea may he 
gain of his world ? 

Of course he has not the slightest idea that the wheel moves. 
It is to him very solid and very vast. He can gain little idea 
of its extent. It will take thousands of generations of baciUi 
even to venture on a guess as to its shape. Perhaps no thought 
can come to him more absurd than the idea that it is round, 
that the great plains and regions of high mountains which he 
traverses with infinite difficulty are the surface of a curve. 
Until he learns to lift a sail before the winds, he can get such 
a little way, anjrwhere. For aught he can see the thing has 
no end. 

He is inquisitive, this micro-man, curious to the last 
degree ; he loves to explore. But it is all so difficult, and he 
has so little time. 

A single electric globe gives him all the light he has, and 
for some curious reason it goes curving around the walls of the 
room, then disappears, to come back on the other side, leaving 
him half the time in the dark. Moreover, it does not describe 
the same circle across the ceiling all the time, but its path 
moves up and down, with the apparent effect of his being most 
uncomfortably cold when it is down and beastly hot when 
it is high. 

PuzzHng over this foolish arrangement, he notes that this 
wobble has a seeming regularity ; and using the alternate 
appearances and disappearances of his luminary as a unit to 
count with, finds that through about two hundred light and 
dark times he is warm and things will grow, and then for about 
two hundred more life is rather dull. Finally, observing the 
thing carefully through a great many wobbles, he concludes 
that there are very close to 365 alternations from the lowest 



MICRO-MAN 43 

point the lamp touches in its circle to the highest and back 
again. It is a stupid number, and it doesn't much matter any 
way ; it is enough to know roughly, so he can plant his crops. 

For the rest food is hard to get, and there are great famines 
and terrible plagues, when the microbes die like sheep — among 
them the microbes he most cared for ; and the newer generation 
does not seem the same. Then, too, other and more powerful 
microbes make war on his little tribe, slaughter his friends, 
carry off the maiden microbes to be harlots and the fine strong 
youths to be slaves. His home is pillaged, and it takes a long 
and painful effort to get on his feet again. The burden of taxa- 
tion imposed by the imperial microbes who govern seems 
to grow heavier year by year ; he borrows, the money-lender 
besieges him, his goods and chattels are sold to satisfy his debts, 
and aweary of the game, and taking consolation of his poets, 
he reflects on the vanity of existence. Sixty or seventy wobbles 
of his lamp through the sky and he is old, and though the time 
seems long, and he is weary, weary, what has it profited, what 
has he learned ? 

What could he learn ? What could he know ? Three hundred 
and sixty-five turns of a wheel going at 5000 revolutions per 
minute — that is, about four seconds of our reckoning ; and 
seventy times four seconds — that is, nearly five minutes. Not 
very long to learn what is this lamp that circles the ceifing and 
makes his nights and days ; not very long to discover that 
he is on the periphery of a wheel — or, if you prefer, of a top 
that spins carelessly ; not very long to figure out that the 
curious up-and-down wobble of the lamp is the effect of the 
whole wheel he is spinning on being in its turn spun round the 
lamp (how incredible !) ; not very long to come at last to 
believe that not only this swiftly turning wheel, but even the 
lamp round which it revolves, and all the objects of the room, 
are being rushed along as in an express train, where, were he 
big enough, he might look out of the window and see the land- 
scape flying by. 

Not very long ! How difficult to imagine that man is no 
better placed ; that he is a being as microscopic to the world 
into which he is born as this fanciful bacillus-man to us ! 

There is here a point of view worth the effort to attain. 
Let us take the matter in another way ; let us turn the illustra- 
tion quite about, just as Swift in Gulliver has done. But 



44 THE WORLD MACHINE 

instead of his Brobdingnagian giants, let the imagination soar 
a little. 

In his rather imitative tale of Micromegas, the nimble pen 
of Voltaire has sketched a traveller from a vast planet which 
is satellite to Sirius, and who on our dwarfish world skips lightly 
over the mountains and across the seas, as a goat from crag to 
crag. We may take a yet wider range. 

Upon some clear moonless night, scintillant with the crowd 
of flaming stars, let your vagrant fancy roam the ways of space, 
there to picture, if you will, some gigantesque voyager from 
another realm than our own, distantly watching from the rail 
of his uncharted vessel the ceaseless turning of the silent earth. 
Directing his helmsman to parallel its course, he notes, as it 
turns and turns, here and there upon wide wastes which, from 
the briUiant reflection of their surface, he may conjecture to be 
oceans, faint specks. These, as he directs his glass to study 
them, seem to trail a thin blackish ribbon behind them. As 
with each successive turn of the earth they come again in view, 
he perceives that they have advanced a little toward one side 
or another of the mirror-like surfaces, finally to merge them- 
selves in the dark patches which he may take to be land. 

Puzzled at the capricious course of these moving speck^, 
which, though regular in their motion, seem governed by no 
law, he signals the man at the wheel to draw nearer. Again 
searching with his glass, these specks take on the appearance 
of drawn-out egg-shells, and he finds that the trailing ribbon 
is a band of smoke. Though swiftly whirled from his view, 
he can yet determine that whichever way they go they pursue 
a fixed direction ; failing to observe any means of propulsion, 
he must nevertheless infer that they have inside some pro- 
pelling mechanism, and are in some way steered. 

Curious and delighted at the thought of an intricate 
mechanism so marvellously small, he approaches his vessel as 
nearly as he dares to this rapidly turning ball, to follow whose 
flight through space he finds it needful to stoke his own engines 
smartly to keep up. With what excited pulses, with what 
genuine awe, does he perceive, in the brief moments that he 
can hold them in sight, that the decks of these traiUng egg- 
shells are covered with other moving specks ; gradually he 
makes out that they are slender midgets, scarce larger to his 
eyes than the harvest mites that we may feel, but hardly see. 



MICRO-MAN 45 

chasing over the back of our hands ; he smiles as he sees them 
dexterously balancing themselves on but two legs, instead of 
six or eight as other insects have. 

Scanning closely, he beholds some of these microscopic 
beings lift their arms in the air and apparently point some 
object at the stars. Are they observing ? Are these telescopes ? 
Can these animalcules, then, reckon their way thus across the 
seas ? How curiously he will think of them ; what enchanted 
little eyes they must have ; and in their microscopic brains 
what thrills must run ! Upon the decks they go about in pairs ; 
when the egg-shells have reached the shore he cannot follow 
them upon the dark land ; they disappear, and yet he may not 
doubt that there they draw out the accustomed course of life 
— mate and have their homes, beget their kind and die. 

As he steers away, to voyage on past Neptune and the dark, 
I imagine him inscribing in his notebook : " Travelled some 
time to-day alongside a considerable-sized globe, largely covered 
with water, and revolving at a high rate of speed. Was able 
to note upon its surface with the aid of my powerful new tele- 
magnafecit an extraordinarily minute two-legged ant, certainly 
able to build and scientifically to navigate vessels at least a 
hundred and forty times his length, and therefore more than 
three million times his bulk, and probable weight. I seemed 
to go from wonder to wonder. How strange and fascinating 
this cosmos grows to me as I journey and learn ! " 

There are heavy types of minds to whom lively illustrations 
of this sort are repellent. Yet, thought of thus wise — these 
mating, building, navigating ants, able to strut about on two 
pipe-stems and not fall — is it not, after all, a marvel of marvels 
what they have done? Shall we not wake to a new sense of 
his achievement : this bacillus man, so infinitely little, set 
against the universe he is learning to map ; so slight a thing, 
the ephemeron of a moment on the dial face of time, a butterfly 
fluttering through an unheeded hour of the cosmic day; so 
slight and weak a thing, cringing with terror before a storm, 
beset with ills, the prey of fear, strange and hapless estray of 
fate's designs ! Do we not grow to a deepened respect for 
what his reasoning brain has forged — for that long-drawn-out 
chain of observation and inference, of comparing, combining, of 
measuring, imagining, of theorising and trying out, which hnk 



46 THE WORLD MACHINE 

by link builds up that corselet of ordered knowledge we call 
science ? Consider his lowly beginnings ; think how handi- 
capped man has been, how he has gone wrong, lost the way, 
stumbled, been led astray, in his long endeavour " to strike 
out a pathway toward the light " ! 

Think of his tools ; he has eyes to see with, hands to feel ; 
sound, taste, and smell are of little use. Measures of the eye 
do not turn out well, so he learns to mark off his fields in lengths 
of his feet or his stride ; distances are a day's march. His 
eyes will see but a little way, and will show only objects com- 
paratively immense ; it is centuries before he hits on spectacles, 
and with these contrives the fernrohre, the " distance-tubes " 
of Hans Lippershey, of Zacharias Jensen, and the microscope 
as well. 

His two hands are clumsy, and do not readily distinguish 
between two weights of silver or gold — he devises the balance ; 
his sense of time is vague — he invents a time-machine, and 
the Roman slaves who run to the Forum to learn the noon hour 
give way to the clock. Patiently he ekes out the meagre 
endowments of nature, until at last amid the wilderness he 
has a workshop. And all the while he reflects, compares, " in- 
tends his mind." He ponders the changing length of nights 
and days, the order of the seasons, the position of the sun, the 
growth of the crops ; he notes the course of the planets, of the 
moon, the nightly wheeling of the firmament round its central 
pivot star ; through the whole concourse and spectacle subtly 
he begins to trace a connection, a binding chain ; he perceives 
that in one way or another they are all linked together ; he rises 
at last to the vast conception which embraces all phenomena in 
that unvarying sequence which he will come to call law. He 
attains at last to a perception of causal relations, within whose 
unbroken series the whole order of events is enchained. He 
pictures the universe as a mechanism ; for chance he substi- 
tutes fate. 

This is achievement sublime ; how did it come ? 



CHAPTER IV 

THE BEGINNINGS OF CERTITUDE 



Unto the angel of the church of Ephesus write ; These things 
saith he that holdeth the seven stars in his right hand, who walketh 
in the midst of the seven golden candlesticks. 

And unto the angel of the church in Sardis write ; These things 
saith he that hath the seven Spirits of God, and the seven stars. 

And I saw in the right hand of him that sat on the throne a 
book written within and on the back side, sealed with seven seals. 

And I stood upon the sand of the sea, and saw a beast rise up 
out of the sea, having seven heads and ten horns, and upon his 
horns ten crowns, and upon his heads the name of blasphemy. 

Revelation ii. i ; iii. i ; v. i ; xiii. i. 



CHAPTER IV 

THE BEGINNINGS OF CERTITUDE 

Primitive man, we have learned to know, differed but slightly 
from the primitive man of now — that is to say, he was in little 
distinguished from an animal. Perhaps in a way the difference, 
even now, is not large. If in the course of fifty or a hundred 
thousand years he has become the " good gorilla " of Buff on, 
we may imagine in the beginning he was the gorilla without 
being good. He answered to the crazy ideal of Nietzsche ; he 
was simply the " blonde beast," save that primitively, per- 
chance, he was not blonde. 

We have his portrait in the famous painting of Gabriel Max. 
The likeness is idealised, no doubt ; the reality would have 
shown less of the age-old pathos that shines in the eyes of these 
our brute forbears ; there would have been more of ferocity. 
He was a savage, with a savage's joy in killing things ; he was 
a thief, a glutton, and a cannibal. To him nothing was for- 
bidden, nothing was criminal. The idea of murder, rapine, 
pillage, torture, or incest brought no feeling of revolt, of disgust, 
or of injustice. They were the simple, natural instincts of 
the blonde beast. He was brutal, he was treacherous, sensual, 
lawless. 

As he multiplied he split in roving bands ; these grew into 
tribes, the tribes into nations. Association brought organisa- 
tion. As food grew scarce, harder to get, he learned to herd, 
then to plant. With his flocks of animals, with his rude fields, 
came ideas of property. To preserve his own he united to 
stop thievery and plunder. This property right, at first tribal, 
became individual. Along with this had grown the idea of 
family. The woman was associated as part of his property ; 
she was his chattel. He was primitively polygamous, no doubt 
gregarious. Eventually, individualising instincts, the sense of 
personal possession, brought a rude morality. He began to 

49 D 



50 THE WORLD MACHINE 

develop ideas of right and wrong. These, established by custom, 
finally became law. He had organised the primitive state. 

Long before this he had learned to cook. The chance dis- 
covery that in cocoa-nuts, cracked and exposed to the air, the 
milk became bitter and produced a singular feeling of exhilara- 
tion, made him a brewer. He became a worker in mud and 
clay. In due time he learned to chip flints, to fashion weapons, 
then implements. 

The discovery of fire was the most momentous event of 
his early history. By this means he became a chemist, a potter, 
a worker in glass, a metallurgist, eventually a mechanic. In 
the beginning these were doubtless the occupations of the 
slave. Nature's nobleman, the blonde beast, despised work. 
It was easier to steal, more exciting to hunt. His natural 
instincts of cruelty and lust were glutted by the rape and slaughter 
of other tribes ; the portions that remained were made menials 
and serfs. Slavery was the universal characteristic of primitive 
brute society ; it survived throughout antiquity. All the so- 
called civilisations of the Mediterranean basin, from the earUest 
of the Egyptians to the latest of the Romans, were founded 
upon slavery. 

It was doubtless a world-wide characteristic. To work was 
ignoble, and it is curious to see how this primitive idea of nobility 
has survived among the property-holding classes of aU times. 
The British land-holder despising " trade," the dilettanti and 
drones of all classes deploring the invasions of " commercialism," 
are a late survival of a society that was archetypal to Plato 
and his kind. From the beginning, human associations seem 
to have been made up of an aristocracy of spoliation and a 
proletariat of service. It was only with the invention of the 
steam-engine, the introduction of machinery, the enhancement 
in value of labour, the cheapening of its products, that the 
mass of humankind was manumitted from its world-old con- 
dition of essential serfdom. 

It is easy to see that it was the slave, the worker, who, to 
lighten the burden of his lot, was the inventor, the improver, 
and out of this the observer and the experimenter. The hands 
which fashioned the primitive grist-mills and water-wheels, 
that lifted the first sails, that devised the rudder, that learned 
to hitch a forked stick to an ox and with it to stir up the ground, 
were the hands of the serf. The occupations of the strong, 



THE BEGINNINGS OF CERTITUDE 51 

the rich, the noble, were to hunt, to fight, to win more property 
by pillage, to make more slaves by conquest. 

It is to the slave, then, in all likelihood, that we owe the 
beginnings of experimental knowledge. His simple inventions 
and contrivances would have sharpened his wits, trained his 
mind, taught him a rude cunning, developed him intellectually 
beyond the brute brain of his brute lord. In due time he would 
have acquired a knowledge of herbs and simples, and become 
something of a physician. His dexterity in cutting up the 
prizes of the chase would have made him the first surgeon. 
His knowledge of cooking and the effect of fire would have made 
him the first metallurgist. Out of this sprung the beginnings 
of alchemy. The natural lust of wonder, of mystery, would 
have early converted these into a primitive diabolism. To 
the heavy brain of his overlord, sodden with gluttony and strong 
drink, it would have readily seemed a black art. The slave 
would not have been long in discovering that in his weakness 
he had found strength, and that his intelligence had given him 
power. 

From this would have come the medicine-man, the sooth- 
sayer, the mage, the priest. A portion of the social fund would 
have been set aside for their support ; they would have become 
teachers and prophets, workers of miracles, diviners of omens ; 
they would have been the interveners between the tribe and 
the evil spirits which populated the air, the nooks of the forest, 
the running streams, which came in the tempest, the thunder, 
the flash of the heavenly fires, and the shakings of the earth. 
The stages of this evolution are all to be traced in that con- 
venient image of past days which we call anthropology. There is 
scarce any phase which may not be illustrated from living tribes. 

It is easy to see that this slave element, become priest element, 
would have laid hold of every available means for the furtherance 
of its power. Foreseeing in a dim way that the origin of this 
lay in a knowledge of phenomena and, in a slender way, in 
devices for the control of phenomena, the more prescient among 
them would have observed attentively the varied processes at 
work about them. 

This is not saying that the higher knowledge was wholly of 
slave origin. Obviously a large part of the human experience 
upon which it is based was a racial experience, with which the 
immediate occupations of the social units had no concern. 



52 THE WORLD MACHINE 

Long centuries, millenniums even, doubtless elapsed between 
what we may term the tame gorilla stage and that in which 
the wonder-working slave had become augur, astrologer, 
alchemist, and austromant. It was long ages later still when 
from these rude beginnings, more than half mysterious, we 
may imagine, even to their practisers, that anything like a 
rational world conception, to say nothing of a mechanical world 
conception, could arise. Let us look about for the first steps. 

Sometimes in the history of ideas the history of a word may 
shed a deal of light. It is of some curious interest to know 
that once learning, knowledge, and mathematics were one. This 
indeed was the meaning of the Greek verb mathemata, " to 
know." For the rest, one of the most primitive of human 
needs was a method of counting. If we look about a little we 
shall perceive that the earliest idea of fixity, of certainty, of 
inevitable sequence, must have arisen from the sense of fixity 
of numbers. 

When man had learned to put together 2 and 2, to subtract, 
to multiply, and divide, he must have seemed face to face with 
a great light. Mere numbers now seem to us such lifeless 
abstractions, that the idea they could have once been almost 
the basis of a religion seems absurd. We know, however, that 
this was true. No doubt a curious sense of coincidence — that 
is, of mystery — must have come to the first man who noted 
that the first four figures of the counting scale, put together, 
sum up ten. Remember that all systems of notation were 
decimal systems, arising from the chance number of fingers 
upon the two hands. The Pythagoreans named the first four 
figures the " grand tetrad." There was a similar mystery about 
the number " seven," the number of planets or " wanderers " 
observed in the sky. The perfect number was twelve, doubtless 
because to them there were twelve lunations in the year, and 
because it divided into so many even parts. Even to Plato, 
numbers seemed the basis of all things. 

Long before this a system of notation had been devised ; 
its beginnings were crude enough. A single stroke counted for 
one, two strokes set side by side for two, and so on. This grew 
very clumsy before many digits had been told off, so various 
combinations were tried. The Babylonian character for ten, 
Grotefend believes to have been a rude picture of the two hands 



THE BEGINNINGS OF CERTITUDE 53 

as they are held in prayer. Little by little, in what manner is 
hidden from our view, grew up the complicated systems which ap- 
pear in the earliest of the clay tablets which have been unearthed. 

It must have all been very old. Some of the Sumerian 
inscriptions, forerunners of the Babylonian, reveal the existence 
of a sexagesimal system — that is to say, in which the count 
extended up to sixty and there begins over again. It was long, 
probably, before the count extended up to a hundred and began 
again there. But why was this especial number of sixty chosen ? 
We can only conclude that by this time something of the pro- 
perties of circles and radii had already become known. This 
in turn had obviously come from their endeavour to forefigure 
the year, the path of the moon, and all the hke. 

Doubtless the earliest of external phenomena which ancient 
man came to study with attention was the changing length of 
nights and days, the succession of heat and cold, the return of 
the seasons. When he had begun to seek a more stable food- 
supply than from the precarious providence of nature, he needed 
a sign for the time to plant his crops. When he had organised 
into tribes and perhaps begun to barter his labour for produce, 
there came the need of a means of reckoning time. The going 
and coming of the moon gave him a unit for a bundle of days. 
He needed a larger, which should fix the return of spring. 

As he watched the heavens he saw that the position of the 
stars at nightfall and at dawn, with reference to the sun, appears 
to change. It was a generalisation of a high order when he 
had reached the conception that the stars are stable, and that 
it is the sun, the bringer of the day, which in reality changes 
its place. Attentively observing the changing rising point and 
setting point of the sun, the primitive astronomers saw that 
it swept through a seeming circle in the air. From this 
perhaps came the Latin word for the year, annus, whence our 
word '' annual," meaning a " ring " ; it appears primitively to 
have signified simply a " bending." The sun in his shift of 
position seemed to describe a continuous bending, which in 
the end brought it back to the same point. 

The reckoning doubtless was not very close ; there was a 
convenience in round numbers. In the beginning they appear 
to have fixed the number of days within this period at three 
hundred and sixty. Doubtless from this the study of the 
circle began. When they had found that a regular figure of 



54 THE WORLD MACHINE 

six sides, each equal to the radius, could be described within 
every circle, it was natural that they should make such a 
division. Doubtless the earlier division had been into the 
twelve periods corresponding to the twelve lunations which 
their crude observations taught them to believe made up the 
year. The change of division marked the separation of the 
theoretical from the practical. 

The three hundred and sixty divisions of the circle were 
named steps, or degrees. As their observations grew more 
accurate they split each of these into sixty parts, partes minutce, 
whence our minutes ; these into sixty more, partes minutce 
secundcB, whence our seconds. The day and the night they 
divided each into twelve parts, corresponding doubtless to the 
twelve divisions of the year. The first time-keeper was the 
sundial ; its face was half a circle. It was natural that they 
should have employed these minor divisions of the circle to 
mark the subdivisions of the hour. 

Along with this application of numbers to time came a 
parallel application to weights. Primitive man had made 
another prodigious step when he had discovered the principle 
of the balance. Our word " pound " comes from the same 
root as " pendant," meaning " to hang," that is, " to weigh." 
The ounce was the twelfth part of this, and meant simply the 
twelfth part ; it is the same word as inch. 

Even earlier must have been the application of numbers to 
measures. There was need first of all to define the exploits of 
the chase or of the march ; this would evidently be in units 
of the distance an ordinary man might cover, travelling steadily 
through the day. With fixed habitations and the subdivisions 
of fertile areas into definite plots came corresponding sub- 
divisions of the day's march. It is evident that the handiest 
units were the average length of feet and hands. It is a rather 
curious reflection of our Saxon civilisation that alone among 
the nations of the earth we should still be employing as our 
unit of a length the human foot, just as did the primitive folk 
of twenty or thirty thousand years ago. Up to within a recent 
time the French measure of an inch was the pousse, the thick- 
ness of a thumb. Fractions of this were expressed in lengths 
like our English barley-corn, just as a single grain formed a 
subdivision of the ounce in weight. 

A pace was simply a step, a yard was a club or stick, doubt- 



THE BEGINNINGS OF CERTITUDE 55 

less of the same length. A stadium was simply a " stage " — 
that is, about the distance that one man could readily shout 
to another and be understood. When they had need of news 
more swiftly than it might be carried by horse or man, a line 
of shouters were stationed at intervals, sometimes over long 
distances. It was thus that word of the disaster at Thermopylae 
was brought to the Persian king. 

When these units of measure had been grouped up into a 
rude system, it is obvious that through a growing proclivity 
to barter must have come a growing sense of the fact of pro- 
portion. When for so many horses or slaves or wives a man 
traded so many skins or sacks of wheat, or weights of meat 
or roods of land, there came insensibly a sense of abstract 
values — that is, the relations of units of one kind to units of 
another. There would be an inevitable comparison of signs 
and symbols representing like quantities of different things. 
From this would have come an intimate sense of the fixity of 
numbers, and likewise of their inter-relations. 

It was a far higher step when he had come to perceive that 
one number might bear the same relation to a second as a 
third to a fourth — our familiar rule of three. The utilisation 
of this method must have been among the earliest instances of 
that method of prevision and subsequent verification which is 
in a sense the foundation of exact knowledge. 

The application of the method must have been very slow. 
There is a legend preserved by Diogenes of how Thales, the 
wise man, when he went among the Egyptians, showed them 
a simple means of measuring the height of the Pyramids. This 
was by measuring the length of the pyramid's shadow at the 
moment that the shadow cast by a staff equalled in length the 
height of the staff. Doubtless the story was a fable ; it may 
have been merely Thales' own boastfulness ; the boasting trait 
is strong in primitive man. The Pjnramids are still a marvel 
of constructive accuracy. The base of the Great Pyramid 
is 756 feet on each side, and so near to a perfect square that 
the mean error of the four sides is only six-tenths of an 
inch. The height is to the total length of the sides as the 
quantity symbolised by tt to the circumference of a circle ; and 
there are other indications in the interior that the ratio of ir 
was accurately known. The P57ramids were built several 
thousand years before Thales was born. 



56 THE WORLD MACHINE 

We have in the fable, then, either an evidence of the extreme 
slowness of mental development, or else an indication of the 
stage attained by the Greeks of Thales' time. 

The construction of the Pyramids indicated a very consider- 
able knowledge of geometry. Its birth must have been far 
back. Herodotus would have it that it was the invention of 
the Egyptian king who wished to give an equal measure of 
land to each of his subjects. Those who dwelt along the Nile 
suffered from the erosions of the river's annual flood, but in 
unequal degree. There was need, therefore, of an annual 
equalisation. This was the work of the harpedonaptce or " rope- 
stretchers." These may have been the first surveyors. Pro- 
bably their art had existed in a rude form for many thousands 
of years. There is in the British Museum a hieratic papyrus 
dating from before 1700 B.C., and founded upon an older work, 
believed to date from before 3400 B.C. This manuscript treatise 
of old Ahmes implies a rudimentary knowledge of proportion, 
squares the circle with very fair approximation, and contains 
many rules of much practical value. It contains no theorems. 

Apparently, then, we might believe that, among the Egyptians 
at least, abstract reasoning — that is, mathematical generalisa- 
tions — did not exist at this period ; and we know of no other 
people then flourishing who were further advanced. The fact, 
however, is by no means certain. We know that among the 
ancient Egyptians learning was confined very largely to the 
priesthood. They guarded their treasure jealously. Know- 
ledge did not ope her ample page to the vulgar. So it was 
even among the earlier Greeks. The Pythagoreans constituted 
a sort of secret society, and in times of distress or disorder 
they were mobbed and their homes burned. 

It may very well be, then, that the manuscript of Ahmes 
does not represent the intelligence of the time any more, let us 
say, than Mr. Gladstone's theories of creation and allied subjects 
represented the intelHgence of his day. The mode of tradition 
may have been almost exclusively, as we know it was largely, 
oral. When the curtain lifts upon Greek geometry, we find 
it far advanced. Euchd is its culmination. Behind him we 
know of a long line of geometers. They in turn may have 
been the successors of a still longer line, reaching far into the 
mists of antiquity. The fact may always be that there came 
at this period a sudden flowering of the human intellect, like 



THE BEGINNINGS OF CERTITUDE 57 

unto that of Europe after the long sleep of Christendom. The 
more clearly we are able to trace any especial development, 
however, the more we discover it to be genetic and even, rather 
than saltatory or precipitate. 

Be this as it may, we know that by the time of Thales and 
Pythagoras methods of geometrical reasoning had taken deep 
hold. They stirred to a singular enthusiasm as well. Professor 
Benn remarks illuminatively upon the lively emotions that 
must have been excited among an intelligent people when 
squaring and cubing, the construction and equivalence of 
figures and the like, was just as strange and wonderful, and in 
another way much more rare, than the electric light dynamos 
and their kindred, a generation ago. There is a story of how 
Pythagoras sacrificed a hecatomb, a hundred oxen, in honour 
of his discovery of the theorem of three squares — that is, as to 
the equivalence of a square on the hypothenuse of a right- 
angled triangle. It is a little doubtful, for Pythagoras was a 
vegetarian and opposed to the shedding of blood ; but the 
same story is told of Thales — so we may take our choice. A 
mathematical training came to be considered a mark and even 
necessity of culture. 

We do not ordinarily think of Plato as a careful reasoner, 
and the puerile phantasies with which his pages are strewn 
do not give us a very high idea of his powers of mind. Never- 
theless, his contributions to geometry were not few, and when 
he set up his academy at Athens, it will be remembered that 
he wrote over the door : — 

" Let no one enter here who knows not geometry." 

By the time the Ptolemies had set up their line of Greek 
kings in Egypt, the science had attained a high dignity. We 
may recall the rebuke of Euchd when the king asked for an 
easier path to learning than through mastery of his everlasting 
theorems : — 

" There is no royal road to mathematics." 

The power of the new weapons found its highest exemplar 
in Archimedes, greatest mathematician of antiquity. It was 
while solving a geometrical problem, at past seventy, that 
he was struck down by a Roman soldier. Spite of all the 
mechanical marvels which he devised, we know that he selected 



58 THE WORLD MACHINE 

as his chief title to fame the inscription of the cyHnder within 
a sphere, and it was this figure' which in after years made known 
his tomb to Cicero. 

The development which the science has taken, especially 
since the introduction of the decimal system, the discovery of 
logarithms, and the like has been extensive. Beside it the 
mathematics of the ancients seem in many ways crude enough. 
The management of their systems of notation, in multiplication, 
in division, to say nothing of their struggles with fractions, would 
be to us simply distracting. To-day the schoolboy solves 
countless problems with an ease which would have filled Archi- 
medes with breathless admiration. The mere introduction of 
the zero must have simplified operations, as measured by their 
rapidity, at least a dozen times. It seems incredible now that 
its advantages should not have been earlier perceived. There 
is some evidence that the Indian or decimal system was known 
in Europe before the rise of the Arabs ; but it found no general 
introduction until it was borrowed from the Arabs at about 
the beginning of the thirteenth century. It does not appear 
to have been in use among the Hindus earlier than perhaps 
the fifth or sixth century. It was certainly not known either 
to the Greek or Latin mathematicians. 

We gain a glimpse of the time from the fact that the clumsy 
abacus was then in universal use, as it is among the Chinese 
still. It consisted simply of beads or pebbles strung on parallel 
rods. Our word " calculate " from calx, " a stone," is a survival 
from this rude counting- machine. They had no algebra even ; 
although Aristotle and even old Ahmes employed letters to 
represent indeterminate quantities, the swifter use of algebraic 
equations did not come in until some centuries later. Here, 
as elsewhere, we perceive the exceeding slowness with which 
new methods and new devices make their way. 

Despite the crudity of their devices, our respect for the 
ancient mind is heightened rather than dulled by the applica- 
tions which they made of the means at hand. In this later 
time we have come to perceive that the knowledge of antiquity, 
the range of its ideas, was far more extensive than had long 
been supposed. The high development of Greek philosophy, 
itself no doubt more or less a rescript of a yet more ancient 
time, is sufficient evidence of the ancient's capacity for abstract 
reasoning. In the pages that follow we shall find many acute 



THE BEGINNINGS OF CERTITUDE 59 

and astonishing examples of their powers in the far more diffi- 
cult analysis of phenomena. Their employment of mathematical 
methods was constant, its applications were wide. 

One of the earliest was the geometry of light. It must 
have been recognised far back that light travels in straight 
lines, and that its reflection has a sharp angle, equal in value 
to the angle of incidence. These facts were very early utilised 
in fixing the positions of the heavenly bodies and in effecting 
the beginnings of our cosmic knowledge. They are still the 
source of by far the larger part of our information as to the 
world in which we live. 

By means of the eclipses men were able to understand that 
the sun lies back of the moon, and to unravel the mystery that 
lay in the puzzling and apparently inexplicable motions of 
the planets. It was by means of the eclipses, as we shall see, 
that a little later the Greeks were able to gather some idea of 
the relative distances of the moon and sun, some idea of their 
respective grandeurs as well. 

It must have been very early that attentive minds observed 
that the light of the sun comes to us in practically parallel 
lines. On the day of the solstice when the sun seemed to stand 
stiU in the heavens, then began its winter retreat, there was a 
belt of considerable extent, several hundred stadia in width, 
in which perpendicular objects cast no shadow. This zone lay 
across the middle reaches of the Nile, just where Egyptian 
civilisation attained its highest efflorescence. The fact must 
have been deeply pondered by the observing priests. Its 
implications could hardly have escaped their wondering minds. 
A few hundred years later it seems to have been employed 
by Poseidonius to compute the distance of the sun, with an 
approximate success that is stiU amazing. 

When we trace out the history of ideas we find as a rule that 
their lineage is long. In some of the earliest of Greek manu- 
scripts that have come down, and again in the pages of Cicero, 
of Cleomedes, and a dozen others of that later day, we find 
perfectly correct notions of the earth and its immediate sur- 
roundings. These conceptions, analogy leads us to believe, 
must have been very old. 

Inferences of such moment, deductions of such power, imply 
that far in the ancient time the idea of fixity in phenomena 
had been deeply impressed upon at least a slender body of 



6o THE WORLD MACHINE 

minds. This was largely fruit from the application of exact, 
that is to say mathematical, methods of reasoning. To it, one 
set of phenomena in especial must have powerfully contributed. 
This was the regularity of recurrence in eclipses. When our 
knowledge of a given set of phenomena is so certain that we 
may rise to the prediction of future events, there comes a con- 
sciousness of certitude which can be inspired in no other way. 
The art of ecHpse predictions was known among the earliest of 
the Greek philosophers of whom we have authentic report. 
The successful issue of a venture of this sort made Thales seem 
to the simple mortals about him a god-like intelligence. In a 
larger sense than that in which it was conceived 15y the marvelling 
lonians this expressed a literal truth ; for among the attributes 
which we may conceive of divinity surely a knowledge of the 
past and of the future must be one. The same story is told of 
Democritus of Abdera. Both of them had dwelt long in Egypt. 
Doubtless it was from the Egyptian priesthood that both of 
them had borrowed their art. It was certainly known among 
the Chaldeans hundreds of years before. 

We know, too, that mathematical methods were very early 
apphed in physical investigations, notably to that of sound. 
Whewell gives high credit to Plato as having been among the 
first to teach that phenomena were capable of numerical treat- 
ment, as opposed to the empty definitions of philosophers like 
Aristotle. In this he was but a disciple of Pythagoras, and 
Pythagoras in turn had drunk of the founts of ancient know- 
ledge, that is to say, of Eg5rpt. 

Of far greater moment was the application of geometry to 
the determination of the figure, and eventually the measure of 
the earth. It was the first step in a true knowledge of the 
cosmos — -that is to say, towards a rational conception of the 
world. It carried the mind into regions the feet of man could 
never traverse, that his eyes might never see. 

How, thus hobbled, could he attain to a certainty that aU 
the after flood of years would not disturb ? 



CHAPTER V 

BION AND THE DOCTRINE OF A ROUND 
EARTH 



Is it possible that men can be so absurd as to believe that there 
are crops and the trees on the other side of the earth that hang 
downward, and that men have their feet higher than their heads ? 
If you ask them how they defend these monstrosities ? how things 
do not fall away from the earth on that side ? they reply that the 
nature of things is such, that heavy bodies tend toward the centre 
like the spokes of a wheel, while light bodies, as clouds, smoke, 
fire, tend from the centre to the heavens on all sides. Now I am 
really at a loss what to say of those who, when they have once 
gone wrong steadily persevere in their folly, and defend one absurd 
opinion by another. 

Lactantius (fourth century, a.d.), On the Heretical Doctrine 
of the Globular Form of the Earth. Quoted by Draper, 
History of Intellectual Development. 



CHAPTER V 
BION AND THE DOCTRINE OF A ROUND EARTH 

The parentage of ideas is as a rule obscure. Rarely may we 
trace their primigenial forms ; they grow rather than are bom. 
Empedocles seems vaguely to have antedated the especial ideas 
of Mr. Darwin by a matter of twenty-five centuries. This is 
more or less true of almost all our larger world conceptions. 

In the fifteenth century the generality of men, in Europe at 
least, still beheved that the earth is flat. Some doubted ; they 
were few. It was the old question : Who was there fool enough 
to dream that there could be a race of men on the other side 
of the earth, with their heads pointing downward into the sky ? 
What would keep them from falling off ? So to the court of 
Ferdinand and Isabella, doubtless the most enlightened then 
in Europe, for to it Columbus of preference appealed, the 
arguments of the Genoese navigator seemed novel enough. 
They had been current among the more enlightened people of 
Greece at least four centuries before Christ. 

Indeed for six hundred years after the time of Plato and 
Aristotle, it would probably be difficult to find a single in- 
structed writer teaching any other doctrine. The beliefs of 
Alexander or of Caesar, of Demosthenes or of Cicero, in this 
differed in no material way from those of Napoleon or Mr. 
Gladstone. Whence did the idea come ? 

It seems older than history ; older, no doubt, than the 

Pyramids. To the very earliest of Chaldean and Egyptian 

observers it was clear enough that the earth did not extend 

endlessly in space, for the sun, the moon, the stars revolve 

about it. And if the earth is not infinite in extent, then it 

must have some shape. But what ? The simplest notion 

undoubtedly was to think of it as flat, perhaps as a flat disk, 

resting on the water. That was the belief of the Chinese, the 

Hebrews, and other primitive people, just as it is the belief 

of such savage tribes as have reached a similar stage of culture 

63 



64 THE WORLD MACHINE 

now. And this idea held the field for a long time. Much that 
is among the highest in human development had been attained 
before men ceased so to believe — the Parthenon had been built, 
the songs of Homer sung, the tragedies of Euripides enacted ; 
Socrates had drunk of the hemlock. 

But to men habituated, hke the early shepherds, to watch 
the heavens night by night came suggestions of another sort. 
The vault of the sky seems a sphere. The stars seem to revolve 
in circles, the horizon is always round, the shadow cast by the 
earth in eclipse is round ; it is a little strange that the early 
astronomers should ever have had any other idea than that 
the earth is a sphere as well. 

This was certainly the teaching of Thales, one of the seven 
wise men ; he had it undoubtedly from the Nile priests, among 
whom he had dwelt ; they, we may surmise, may have been 
teaching it to the initiate for ten or twenty centuries before ; 
perhaps for a period more distant from Thales than Thales 
from us. And the astronomy of the Chaldeans was not less 
ancient. Nevertheless their doctrines were not held by the 
generality of men. 

We may fix with a fair degree of certainty when they came 
in, at least to European thought. They were not known or 
not accepted at the time of Athens in her glory, the Athens 
of Pericles and Phidias. They were accepted as a matter of 
fact by Aristotle a century later. Whatever their force, they 
did not prevail in the all-embracing mind of Democritus of 
Abdera — ^he who, save Archimedes, was perhaps the greatest 
intellect of antiquity. They had certainly been worked out 
in full detail by Bion, his pupil, if we may trust to a hint in 
the frugal pages of Diogenes Laertius. 

Of this Bion the mathematician, and native, like Democritus, 
of Abdera, we have only a line. 

" He was the first person who asserted that there were 
countries where there was day for six months and night for 
six months." 

That was all that remained of him to fame, when in the 
second century of our era Diogenes of Laerte came to write 
that curious history to which the larger part of our knowledge 
of the ancient philosophers is due. But consider for a moment 
all that this assertion of Bion's implies. There is not the 
slightest possibihty that the land of the Midnight Sun was then 



THE DOCTRINE OF A ROUND EARTH 65 

known, even by tradition. Though the Phoenician traders 
may have penetrated to the Baltic, there is Httle to suggest 
that there were then dwellers or even voyagers within the Arctic 
circle ; and lands no farther distant than Scythia were peopled 
with the fantastic legends of the Hyperboreans, a race that 
lived in perpetual happiness and everlasting youth. 

Bion's belief, we may conjecture, was rather one of those 
splendid inductions which sometimes arise from a slender array 
of facts. Travel in his day, as in ours, was the correct pro- 
cedure of cultivated youths, and whether or no Bion had crossed 
the seas to Egypt, we know that Democritus, his teacher, had. 
And he who will journey no farther to the south than by the 
breadth of the Mediterranean will note a curious change in the 
position of the stars. The questioning eyes of the Sphinx meet 
other constellations than those of our more northern climes ; 
the pole-star lies lower upon the horizon. Furthermore, one 
discovers that in the southerly regions the days and nights 
are shorter, according as the sun has passed the summer or 
winter solstice, than in the north. At the equator they vary 
little throughout the year. It would be difi&cult to account 
for all this if the earth were a plane. 

As the ships go out to sea, the earliest of observers must 
have noted that they disappear piecemeal. Returning, the 
lights of the harbour are visible from the mast-head some time 
before they may be seen from the deck. Ascending a high 
mountain the horizon steadily widens, and objects that from 
the lower lands lie below it come into view. If the surface 
of the sea and the land is curved, the earth must be a ball. 

Bion was a geometer, something of a physicist too, evidently ; 
he understood in all its implications the geometry of light. 
With him let us draw a circle to represent the earth, set the 
sun at a distance, draw straight lines for its rays, and see what 
will happen. With the sun at a certain height at noon its 
rays will illuminate a certain area ; shift the angle and the area 
shifts with it. 

Let us put it on paper. (See Fig. i.) 

When the sun at noon stands directly in the zenith, the 
days and nights are of very nearly equal length — twelve hours 
day, twelve hours night. It follows therefore that, if the earth 
is round, the sun at a given time illumines just half its surface. 
If now the position of the sun at noon shifts, so that the days 

E 



66 



THE WORLD MACHINE 



are much longer than the nights, as in the northern summers, 
for the other half of the world the days will be shorter, and 
shorter by as much as they are longer in the northern hemi- 
sphere. As you go toward one pole or other the condition 
is intensified. 

So, when the sun is at the extreme point of its northern 
advance, its summer halt or '' solstice," as at S in the figure, 
its rays will cover the northern pole ; from W, the winter 
solstice, they will leave it in the dark. As this shifting of the 
sun's position from one point to the other occupies half the 
year it is clear that from the north pole (N P) the sun will 
be continuously visible for six months and then for six months 
disappear from sight. When the sun stands at E there will 




Fig. I. 

JSJote. — It is needless to say that this scheme is based on the idea that 
the sun circles the earth, as it so doubtless appeared to Bion. 

be equal nights and days all over the earth, save at the ex- 
tremities of the poles. This is our equi-noctes, period of storms. 

Here, then, was a geometrical construction which accounted 
for all the facts of observation. But to do so absolutely there 
was a difficulty to be surmounted. The theory of Bion re- 
quired that the sun be at such a distance that the bulk of the 
earth cuts no figure. For it is clear enough that if the earth 
is very large, and the sun a small body not so very far away, 
the curve in the earth's surface would shut off the sun's rays 
from much more than half the earth, and no day an5Avhere 
would be twelve hours long. In order that the day occupy 
one-half the time from one dawn or one sunset to the next, 
the sun must illuminate half the earth, provided, of course, 
that the earth is really round. And there was no escaping the 
evident certainty of this last. 

More than that, the shadow that falls upon the moon in 



THE DOCTRINE OF A ROUND EARTH 67 

the time of an eclipse required that the sun be larger than the 
earth ; for if the earth is a globe the shadow it throws will be, 
if not a cylinder, a cone, either upright or inverted, as the 
source of illumination is larger or smaller than the earth. Here 
is doubtless another diagram that Bion and others who thought 
about it must have drawn : — 




Fig. 2. 

If the sun were small and near, as at S, then the shape of 
the earth's shadow would be that indicated by the lines S A, S A', 
and the moon in travelling round the earth would be blotted 
out for many hours during an eclipse. This is not the case. 
Often only a part of the moon's disk is cut off during an eclipse ; 
never does it remain in the earth's shadow much more over three 
hours. Occult ations of the sun make it clear that it is vastly 
larger than the moon : it must also be vastly larger than the 
earth in order to realise the conditions indicated in the figure. 

One step further. If the sun be larger than the earth, then 
its distance must be immeasurably vast, for when its rays strike 
the earth they are to all intents parallel. That is attested 
by the fact that the shadows cast by sunlight alike of the 
Pyramids and of a knife-blade, are sharp. And again, if the 
sun were not at a great distance, at points on the earth near 
the poles (P P in the figure), a part of the sun's disk would be 
cut out by the curve of the earth continuously. 

On the other hand, if the sun is larger, and not at a very 
great distance, more than half the earth would be continuously 
illuminated, and we should never have equinoxes and equal 
days, as we do, nor, for example, would the poles have six 
months day and six months night as Bion taught. 

Thus, as it chances often, the elucidation, the bringing into 



68 THE WORLD MACHINE 

the light, of one obscure problem was the illumination of the 
other. The linking of fact to fact which revealed the mechanism 
of the changing lengths of the day brought with it the proof 
of a spheroidal earth. It must, too, have set men thinking 
out the mechanism of the seasons as well. It certainly accus- 
tomed the mind to the idea that the blazing ball which daily 
sweeps through its circle in the heavens is in reality a body 
colossal in its dimensions and therefore fixed at an enormous 
distance. It was among the first of these splendid flights of 
the imagination which have characterised aU scientific advance ; 
it was among the earliest of these difiicult conquests over appear- 
ances upon which all progress of knowledge depends ; it was 
among the first-fruits of that endeavour to introduce mechanical 
conceptions into the explanation of phenomena, upon which all 
science is based. 

Not without a tinge of melancholy will the student of history 
take note of the date ; that among the freest people of antiquity, 
at near two thousand years before Columbus stood disputing 
with the wise men before Ferdinand and Isabella, there were 
thinkers who had made the first steps toward a correct know- 
ledge of the earth, and from whom the superstitions of the 
vulgar, like an outworn mantle, had been cast away. 

Whether all this had been done by the priests of Isis or 
the servitors of Bel, still two thousand years further back, we 
do not know. Among the pyramid-builders of Egypt a high 
level in both astronomy and mathematics had been attained. 
The truly marvellous geometrical construction of Cheops is 
proof of that. Its edges are the four points of the compass, 
determined with astonishing precision, and from the royal 
burial-chamber, in the far depths of the Pyramid, through the 
long inclined tunnel which leads to the entrance, a mirror 
kept ceaseless vigil with the polar star. There is little reason 
to suppose that the genial brain which planned that mightiest 
of human tombs differed in any appreciable degree in either 
its capacity or its scientific knowledge from Archimedes or 
Newton. Men who could thus observe and thus build must 
have been reasoners as well. But if any one among them had 
drawn the figure of Bion, the sands of the desert cover it as 
they cover him. 

Until that figure had been drawn, or until such a train of 
reasoning had been foUowed out, men's ideas about this earth 



THE DOCTRINE OF A ROUND EARTH 69 

could scarce have been less fanciful than those of a Moro 
Islander now. They were woven of dreams, and dreams to 
which, in their essence, the greater part of the human race 
still clings. But at least in the fifth century before Christ, 
while sacrifices were yet offered before the golden masque of 
Pallas in the Parthenon, and the wisest among men still con- 
sulted the oracle at Delphi, to a slender band a vision of the 
truth had come. As the truth spread and the earth widened 
the sacrifices ceased ; the Homeric gods, too proximate to 
men, retired from Olympus to take up their residence in the 
vaguer spaces of the sky. 

In another century Aristotle could note without surprise, 
without even naming the source or indicating the methods 
employed, that the geometers had put a girdle round the earth. 
Not merely its figure but its actual size had been determined. 
How was it done ? 



CHAPTER VI 

ERATOSTHENES AND THE EARLIEST 
MEASURES OF THE EARTH 



The similitude which many have fancied between the superiority 
of the moderns to the ancients, and the elevation of a dwarf on 
the back of a giant, is altogether false and puerile. Neither were 
they giants nor are we dwarfs ; but all of us men of the same 
standard, and we the taller of the two by adding their height to 
our own : provided always that we do not yield to them in study, 
attention, vigilance and love of truth, for if these qualities be 
wanting, so far from mounting on the giant's shoulders, we throw 
away the advantage of our own stature by remaining prostrate on 
the ground. 

LuDovicus VivES ; quoted by Lewes, Aristotle. 



CHAPTER VI 

ERATOSTHENES AND THE EARLIEST 
MEASURES OF THE EARTH 

On a leisurely summer afternoon, as you lie and look up into 
the cloudless blue, one may agree that it is very charming and 
very well done ; so much so that one may easily wish all life 
like that — and usually does ; but it hardly seems very inform- 
ing nor even so very stimulative to investigation. For example, 
who, without a hint from history, would ever believe that there 
is in the sky a simple way to compute the circumference, and 
hence the diameter, the area, and the solid bulk of this globe ! 
— yes, and to measure the obliquity of the ecliptic, or tip of 
the earth's axle to the plane of its orbit round the sun as well. 

Yet Eratosthenes of Cyrene, the myriad-minded keeper of 
the Alexandrian Library under Ptolemy Euergetes — scholar, 
poet, critic, geographer, physiographer, mathematician, in- 
ventor, mechanician, astronomer, wit and sceptic — found a way 
and did it. I have told of this method elsewhere ; as I gaze 
into the non-committal emptiness above me, the marvel of it 
lingers still. 

Watching the sun as it nears the height of the arching blue 
overhead, I note that a post near where I lie casts a slanting 
shadow, as a sundial does. I reflect that if I go southward 
the length of this noonday shadow grows less and less, and I 
know that there is a place where, in the longest day of the year, 
it will disappear entirely. This is when the sun is sheerly in 
the zenith, and has reached its summer station, where it will 
seem to stand still for a few days, then again recede ; the sol- 
stitium of the Latins. If I can find out just how far to the 
south this point lies, it is evident that I hold in my hands the 
solution of the problem. I have only to take out my watch, 
or my jack-knife, hang it on a string and make a plummet of 
it, and holding it over the farthest edge of the shadow cast 



74 



THE WORLD MACHINE 



by the post, measure the angle between the plumb-Une and 
the slant of the shadow thus : — 




Fig. 



It is evident enough that, if the earth is round and the sun 
at a very great distance, the angle that is marked A wiU be 
to all intents the same as if it were taken from the centre of 
the earth. But this means that the angle will cut out the same 
arc in the circle of the sky as, from the centre of the earth, it 
would cut out of the circle of the earth's circumference, as 
another figure will make clear enough : — 




Fig. 4. 

The line B Z is my zenith, the direction of my plumb-line. 
The angle I have measured is the angle marked A, and for a 
rough calculation is the same as the angle C at the earth's centre. 
The arc of the circle S Z is the same as the arc A B on the surface 
of the earth. If the angle A is about 7° 12', the arc A B is one- 
fiftieth of the earth's circumference. If the distance from A 
to B on the earth is 500 miles, then the earth is 25,000 miles 
around. The globe has been measured in half-an-hour. What 
could be simpler ? 

I said above ** It is evident enough." Laplace used to use 
this phrase rather freely in his expositions. Sometimes he 



EARLIEST MEASURES OF THE EARTH 75 

was asked to explain why it was so evident, and it is recorded 
that it often cost the great mathematician half a day to work 
back through his calculations to make the fact clear. Much 
depends on the point of view. Eratosthenes lived at the apex 
of a civilisation inferior in but little to our own. To reach the 
point where his ingenious mind might divine the method I have 
described above was a long travail. Perchance a hundred 
thousand years stood between cave-dwelling man and the 
theorems of Euclid, which enabled the Alexandrian astronomer 
to take the earth in his hands as a vase and say : This is so 
many inches around. 

Was Eratosthenes the first ? Probably not by many cen- 
turies. Aristotle, in the work which has come down to us 
under the title De Ccello, has a line about the geometers who 
had fixed the circumference of the earth at 400,000 stadia. He 
did not have the exact and measuring sort of a mind, and he 
is so little curious of the matter that he gives no hint of how 
it was done. It is not impossible that he did not know ; that, 
£is Bailly conjectures, the figures had been sent him by Callis- 
thenes from Babylonia, when the latter journeyed thither with 
the silver shields of the Macedonian. It is Bailly's idea that 
the measure may have been even of Chaldean origin, and hence 
very old. 

There was a curious tradition, preserved by Achilles Tatius, 
that the Chaldeans had measured the earth in terms of a day's 
march. They said if a man were able to walk steadily, and at 
good pace, he would encompass the earth in one year. They 
counted that he would do 30 stadia (about 3 miles) an hour, 
and so computed the great circle of the globe at 263,000 stadia, 
which was very close to the estimate made by Eratosthenes. 
Whether they employed the same scheme in their measure- 
ments as he did, we do not know. But there were others as 
simple and direct as the Alexandrian's. For example, the 
foundation which bears up the weight of the Great Pyramid 
was levelled with an astonishing accuracy ; and we have already 
noted that the axis of the long tunnel leading from the subter- 
ranean chambers beneath it was directed toward the polar star. 
The lines of this remarkable passage-way and the foundation of 
the pyramid naturally form a certain angle, as the figure below 
will disclose. (See Fig. 5.) 

As the foundation is the plane of the horizon, the angle 



76 THE WORLD MACHINE 

indicated at a gives the elevation of the pole-star above the 
horizon at that point. 

With a party of geometers, here quite literally " earth- 
measurers," we take boat and cross the Mediterranean, and from 
the Mosque of St. Sophia make the same observation. But 
the angle is no longer the same ; the pole-star is higher up 
toward the zenith ; the angle it makes with the plane of the 
horizon is greater. As we have calculated the two angles in 
degrees, then we may subtract the greater from the less ; we 
do so, and find that the difference is about ii°. Instructed 
by Bion, we know that this change is due to the fact that the 
pole-star is fixed, and that we have been travelling over the 
curving surface of a globe. A moment's reflection makes it clear 



to Pole Star/ 

/ 




Fig. 5. 

that these 11° are in reality 11° of a great circle of the earth — 
supposing, of course, that the Christian capital of Constantine 
is directly north of Cairo (it is a little out). We have then 
only to know the distance we have come to calculate the 
entire circumference of the circle. 

This is to all intents the method now employed, and it 
requires for its successful application only a water-level, an 
angle measurer, and a known distance along a meridian. The 
device is practically the same as that of Poseidonius, friend 
and master of the accuser of Catiline. Instead of the pole- 
star Poseidonius chose Canopus, which, viewed from the island 
of Rhodes, just grazed the horizon ; at Alexandria it rose a 
certain height above, and he measured the angle, some seven 
degrees. 

Yet these various measures differed greatly. That reported 



EARLIEST MEASURES OF THE EARTH 77 

by Aristotle was 400,000 stadia ;;^ Archimedes speaks of 300,000 ; ^ 
Eratosthenes' figure was 250,000 ^ (or 252,000) ; Hipparchus 
wished to increase this to 275,000 ; ^ Poseidonius to reduce it, 
fixing it at 240,000 ^ stadia according to Cleomedes, at 180,000 '^ 
according to Strabo. This last figure was that adopted by 
Ptolemy,'' and this and other errors of Ptolemy were the basis 
of Columbus's belief that, India was near. Had he known the 
true distance, possibly he never would have sailed. 

How near was the truth ? We cannot answer, for the 
exact value of a stadium we do not know. The ill-fated Bailly,^ 
and following him (without a suggestion of credit) Laplace,^ 
noting that the varying estimates stand in a simple relation to 
each other, supposed that they might each be the transposition 
of an original measure of great antiquity and great accuracy 
into stadia of varying length. This may be true, but there is 
a remark of Strabo,^^ near contemporary of Poseidonius, some- 
what troublesome to this view, wherein he observes : "If, of 
recent measurements, we prefer those which diminished the size 
of the globe, such as that adopted by Poseidonius ; which is 
about 180,000 stadia," &c. — as against the 252,000 of Eratos- 
thenes. 

If the measures were really different, we may conclude that 
the closest was the latter, and that it was but little out of the 
way. It does not appear that any new measures were made 
in Christendom before those that were made by the French 
physician. Dr. Fernel, in 1517, five years after the ships of 
Magalhaens had returned from their circumnavigation of the 
earth. 

Seven hundred years before, in the golden age of Arabian 
culture, when all Europe had relapsed into barbarism and 
Bagdad shone as a centre of learning and of light, a series of 
measures had been effected on the plains of Shinar and of 

1 De Ccello, ii. 14. 

2 Arenarius, ii., Introduction. 

3 Pliny, ii, 108. 

* Cleomedes, p. 65 ; ed. Blake. 

^ Cleomedes, loc. cit. 

^ Strabo, vol. i. p. 140 ; ed. Bohn. 

7 In his " Great Syntaxis " {Almagest of the Arabians). 

8 Histoire de l' A sir on. Moderne, tome i. 

^ Exposition du Systeme du Monde, Book V. chap. ii. 
1^ Loc. cit., i. p. 114 ; ed. Bohn. 



78 THE WORLD MACHINE 

Mesopotamia, under the khalifate of Al-Maimun. When that 
princely patron of science and letters sat upon the Mohammedan 
throne, Eratosthenes had been dead a thousand years ; so 
long did it take before his ideas, with the voyages of Columbus 
and Da Gama, might come into practical effect in the affairs 
of the world ; so long did the weight of ignorance and a de- 
grading superstition hang over and benumb the minds of men. 

Eratosthenes, we know, was not merely one of the founders 
of astronomy, but the founder of scientific geography. And 
what a widening of horizons the new map of the world, as con- 
structed by the Alexandrian geographer, must have wrought ! 
Means of communication then were slow ; no *' liners " then 
raced straight and swiftly from port to port. Men did not 
venture far. Though there were records of the compass in 
use in China nine centuries back of this, it was unknown to 
the Greek and T5n:ean mariners, who crept along the coast 
of the Sea- In- Media-Terra, the known terra, and out through 
the Pillars of Hercules to Ultima Thule. From the ports of 
T3n:e to the Gateway of the Night was scarce 2000 miles. The 
Hellespont and the Euxine carried the map-maker's stylus 
scarce another thousand eastward. Half this combined dis- 
tance reached from the mythical borders of Hyperborea to 
the fabulous regions of the Upper Nile. The known earth was 
a rectangle of about the present size of the United States. And 
the measures of Eratosthenes made this a scant fortieth part 
of the whole surface of the globe. In his estimate, what was 
known was to the unknown as 39 to i. 

Is it the impression that we have here merely an intellectual 
conception — that the meaning of it in no wise came home to 
any of the ancients — that there was no vivid sense of new 
continents, new worlds to explore ? — Listen, then, to a passage 
in old Strabo ; he is telling of the ideas of Eratosthenes, who, 
he says, held " that if the extent of the Atlantic Ocean were 
not an obstacle, we might easily pass by sea from Iberia 
{i.e. Spain) to India, still keeping in the same parallel (of the 
temperate zone), the remaining portion of which parallel, 
measured as above in stadia (252,000) occupies more than a third 
of the whole circle ; since the parallel drawn through Athens, 
in which we have taken the distances from India to Iberia, does 
not contain in the whole 200,000 stadia." ^ 

^ Strabo, i. p. loi ; ed. Bohn. 



EARLIEST MEASURES OF THE EARTH 79 

Here are the identical ideas of Toscanelli and Columbus put 
forth by the man most eminent in science and learning in 
the most learned, most innovating, sceptical, and restless city 
of antiquity ; and, what is yet more extraordinary, with the 
same erroneous ideas of distance. The Alexandrian figures the 
span from Iberia westward to India at " more than a third " 
of the whole circle. We know now that it is twice this. He 
was misled |by the estimates of the distance from India to 
Iberia, which could only be traditional, and not by his ideas of 
the size of the earth. Seventeen hundred years afterward, 
Columbus and his Florentine proponent, accepting the guidance 
of Ptolemy, were still further from the truth. 

Again, is it to be supposed that, great as was the fame and 
authority of the Alexandrian geographer, his ideas fell upon 
listless ears ? — By no means, for in one way and another his 
Geographica stirred a whole host of commentators and dis- 
putants, among them Polybius the historian and the great 
astronomer Hipparchus. At near three hundred years after, 
Strabo writes a vast work that is little more than a running 
comment on the statements, estimates, and ideas of his pre- 
decessor. Strabo is especially interested in this thought of 
the circumnavigation of the earth, and, apropos of the passage 
given above, offers a curious muddle of prophetic insight and 
logic bad enough for Aristotelian ; but you will recollect that 
Strabo was very old when he wrote : — 

" Here, too, his reasoning (Eratosthenes') is incorrect ; for 
this speculation respecting the temperate zone which we in- 
habit, and whereof the inhabitable earth is a part, devolves 
properly upon those who make mathematics a study. But it 
is not equally the province of one treating of the habitable world. 
For by this term we mean only that portion of the temperate 
zone with which we are acquainted. But it is quite possible 
that in the temperate zone there may he two or even more habitable 
continents, especially near the circle of latitude which is drawn 
through Athens and the Atlantic Ocean " {i.e. the Pillars of 
Hercules). 1 

What an amazing guess ! And consider that aU this was 

from four to seven centuries before the churchly fathers were 

gravely deciding that the earth could not be round, because then 

the folk at the antipodes would be hanging by their feet with 

1- Loc. cit., i. p. 102 ; ed. Bohn. 



8o THE WORLD MACHINE 

their heads downward in the air, which was so manifestly 
absurd ! 

A shorter route to India ; two or more new and probably 
habitable continents ; but one -fortieth of the globe known ; all 
the rest a field for exploration and conquest ! — ^such were the 
broad and alluring vistas which the pages of Eratosthenes 
opened to the adventurous minds of that keen and teeming 
time. One would think that the spirit of the ardent youths 
of that day would have leapt within them to be gone upon the 
quest. It is fairly certain that the continent of Africa had by 
then been sailed about, perhaps more than once. There was 
a time when at its height the University of Alexandria numbered 
14,000 students. On the wharves of the city were exposed 
the wares of a hundred nations. Yet if there was any Columbus 
to stand before the court of the Ptolemies to plead for ships, 
we have no word. Had there been, we may be reasonably 
sure that he never would have waited twenty years ! 

Why was there no one to venture out ? The unknown must 
have beckoned then as now ; their pulses must have throbbed 
with the same fever of the Just- Beyond. But they knew then 
of no strange north-pointing needle to guide them over the track- 
less seas. Perhaps they did not half believe that what this 
gravely jesting old keeper of the books taught was true. No 
revolving cylinders had yet been so contrived as to reproduce 
his papyrus leaves ten thousand in an hour, and spread them 
through the lands ; there were no lithographers to duplicate 
his curious map. All that was done by slaves, as scribes. 
Books cost them like Old Masters now. Trade was despised ; 
and Alexander, immortal in the splendid city he had founded, 
was among the gods. The Incas and the Aztecs might rear 
their temples in peace for fifty generations more. 

But at least the earth had been measured. It was no 
longer endless or indefinite ; it was now a hall, 252,000 stadia 
at near count in circumference. A tremendous stride ; a great 
and splendid piece of work. Above all the Alexanders, Caesars, 
Tadema-Napoleons, I set the brain which first spanned an 
earth, over whose little patches these fought through their 
empty, bootless lives. Why should we have no poets to cele- 
brate so great a deed ? 

But advancing knowledge, which had thus envisaged a vast 
but not immeasurable globe, unsupported by the emptiness of 



EARLIEST MEASURES OF THE EARTH 8i 

space, was not here to halt. The geometrical constructions of 
Pythagoras and Democritus, which in the hands of Bion and 
the Alexandrian had found so fruitful an application, were 
destined to yet wider conquests. If triangulation of the stars 
might thus disclose the size and figure of the earth, might it 
not reach out and span the moon as well — the moon and, yea, 
the sun ! 
But how ? 



CHAPTER VII 

ARISTARCHUS AND THE DISTANCE AND 
GRANDEUR OF THE SUN 



Intellect is the swiftest of things, for it runs through everything. 

Necessity is the strongest of things, for it rules everything. 

Time is the wisest of things, for it finds out everything. 

Thales. 



CHAPTER VII 

ARISTARCHUS AND THE DISTANCE AND 
GRANDEUR OF THE SUN 

Upon some far crag of the Matterhorn, fancy, if you will, that 
a man was born and brought up with no other knowledge of 
the world than what he there might gain. Conceive that this 
crag is surrounded on every side by precipices, shelving down 
thousands of feet to depths hidden by the clouds, so that, by no 
construction he may devise, can he escape. He looks out over 
an Alpine waste, and sees in the distance other vast crags lifting 
their lion heads from out the mist. In intervals of guarding 
his flock of goats, I picture him gazing across the grey expanse 
with a vague longing to form some estimate of how far these 
far-off peaks may be. What idea can he gain ? 

He has no instruments save such as he may carve with' a 
belt knife ; but in his cabin there is a volume of Euclid. 
Stimulated by the attentive study of that Open Sesame to the 
mysteries of space and form, he seeks to learn what he may. 

One day I see him note that, as he holds up his hands to 
scan the mountain-side in search of his flock, he seems to have 
two hands ; he shuts one eye, one of the hands disappears ; 
at once he has begun to work out the theory of vision. He 
next observes that if he holds up his finger at arm's length, 
and with one eye open, sights across it to some object on the 
further wall of his hut, or against the mountains, the position 
of his finger seems to shift as he shuts the one eye and opens 
the other. Try, and you observe the same thing. 

Just the same thing happens when he takes a long walk 
from his habitation and sees two peaks shift in their position 
to each other, as he changes his point of view. Aided by a 
theorem of Euclid, can he combine these new experiences to 
make a measure ? He sits down, and on a smooth chip of 
wood traces this figure. (See Fig. 6.) 

Seen from the door of his cabin, the two peaks, P and Q, 



86 THE WORLD MACHINE 

make a straight line. He walks away to a distant point at M ; 
the two peaks fall apart ; they are now seen under a different 
angle, or, as the astronomers say, they have a different parallax. 
Lines drawn from his new point of view to the two peaks 
and back again to his hut form two triangles, and these are, 
moreover, right-angled triangles. He has then only to measure 
the two angles at M to construct these triangles in right pro- 
portion, and knowing the distance he has come from his hut 
(the line H M), he may quickly compute the respective distances 
of the two peaks. 

The position of the man upon the Matterhorn differs in 
no essential way from that of man upon the earth, save per- 
chance that our isolation is yet greater. We cannot leave the 
crag upon which we dwell, and though it conveniently revolves. 




Fig. 6. 

so that we can see what is underneath it, this is little material 
gain ; we are bound to it as Ixion to his wheel. 

It is evident that, at the time of a solar eclipse, the sun and 
the moon stand in something of the relation of the two peaks 
we have imagined ; so that if, at the moment the moon touched 
the limb of the sun to the eye of one observer, the angles of 
their apparent separation were taken by another at some distant 
point on the earth, it might be possible to reckon roughly the 
relative distances. But science in the ancient times was not 
organised as now. Even in the golden days when the Greek 
kings ruled in Alexandria, they did not send expeditions to 
the Cape of Good Hope, or build observatories in Peru. As 
far as we can make out, there was little co-operation or concerted 
action, which is the very life of modern knowledge ; though the 
great university at Alexandria was an exception, they mostly 
went it alone, unaided by church or prince or state. 



DISTANCE AND GRANDEUR OF THE SUN 87 

Moreover, it was difficult then to get a long base for observa- 
tions, such as their crude measures of angles required. So, 
beginning with the moon, they resorted to the ingenious plan 
of taking its parallax when it lay in the horizon of one point 
of observation. Obviously at this moment the direction of 
the moon was at right angles to a plumb-hne at that point, 
and hence to the centre of the earth, as a glance will show : — 




Fig, 7- 



It is clear that if a second point on the earth, as D, can be 
found where the moon is at the same moment directly on the 
meridian, then a hne from the moon through this point will 
equally pass through the earth's centre. As a matter of fact, 
it would be rather painful work to locate this point, but it can 
be reckoned, and we have again a right-angled triangle in which 
the distance of the moon is given in terms of the earth's radius, 
C H. Ptolemy, in his treatise, describes another simple method, 
and there were doubtless others still. They did not agree very 
closely ; the distance is, in reality, a troublesome quantity 
to compute, because it varies. Its least and greatest distances 
were fixed at from 50 to 85 earth's radii, so that, taking 70 
as a mean, they were not far out. And with the circumference 
of the earth fixed, they knew that the moon was somewhere 
around 240,000 miles from the earth. 

They could likewise note that its apparent or visual diameter 
is half-a-minute, and, the distance known, could compute that 
this mild-mannered orb was in reality a colossal thing — a body 
some 2000 miles through, that is, a quarter of the diameter 
of our massy earth. 

The temperature of the calculating spirit is proverbially 
low ; but if the hand of Newton could so tremble with excite- 
ment as he foresaw that his figures would demonstrate the 
great law he had divined, with what profound amazement must 
he who first computed the moon's magnitude have laid down 
his pen ! This softly glowing disk, whose apparent size is so 



88 THE WORLD MACHINE 

slight that, looked at between thumb and forefinger held at 
arm's length, the fingers nearly close — is this a body so vast 
that it would almost cover the then known world ? — a body 
whose height or diameter is equal to the entire length of the 
Mediterranean, which cost the mariners in their vessels a fort- 
night or more to traverse. And this colossus of the skies swings 
free in space ! It clearly revolves about the earth ! What 
holds it in its place ? — He to whom all this came first would 
doubt the validity of his own computations ; he would be 
unable to realise that such a thing could be. 

And yet, as he reflected, conviction must have come. In 
climbing mountains, whence, in a clear atmosphere, objects 
are visible a long way, he must have noted how, at a distance, 
huge edifices sink away to a point ; a great city, even, becomes 
a patch. But, ascending even the highest mountains, the moon 
draws no nearer. Compared with its elevation above the earth, 
the height of the tallest peaks seems nothing. Certainly it 
must lie afar off ; and if this is true, the simplest of calculations 
enforces the belief that^its bulk is vast beyond belief. Appear- 
ances had again been overthrown. 

It remained to consider the problem of the sun. If the 
eye may be so deceived as to the grandeur of the moon, to what 
conceptions of immensity must the imagination rise to picture 
the extent and distance of the monarch of the day ? 

Here again simple geometrical considerations sufliced to 
establish the groundwork of a just estimate. The sun lies 
behind the moon : the eclipses showed that ; and it must be 
far behind, because the shadow cast by the earth is a diminishing 
cone, and the sun is therefore larger than the earth. If it were 
smaller, the conical shadow would be divergent. The earth, 
they had found, was three or four times in diameter the size 
of the moon ; the sun must therefore be at least six or eight 
times. And yet, averaging the various eclipses, the moon in 
transit just about covers the disk of the sun ; their apparent 
size is the same. 

A body which is eight times another in diameter and yet 
appears to be the same in size, is eight times as far away. If 
the moon is distant about sixty earth radii, the sun must, there- 
fore, be distant at least four or five hundred earth radii. It must 
be at least two million miles away ! How the world was growing ! 



DISTANCE AND GRANDEUR OF THE SUN 89 

So much was self-evident ; was there any way to make an 
actual measure ? The first we know of to attack the problem 
was the predecessor of Eratosthenes in the school of Alexandria, 
a contemporary and possibly the teacher of Archimedes, when 
the young Sicilian went from Syracuse to Alexandria to school. 
This was that Aristarchus who, to Laplace, " paroit etre dans 
I'antiquite celui qui eut les plus justes notions de la grandeur de 
I'univers." He was, as we shall see, the forerunner of Copper- 
nicus ; if grandeur of conceptions be a measure of the brain, 
or ingenuity of its powers, then we must rank Aristarchus with 
Democritus and Archimedes as one of the three or four most 
acute intellects of the ancient world. 

The eccentric actions of the moon, the varying shadow it 
casts, or receives, its so-called inequalities, were then among 
the principal problems of the heavens ; and over them the 
Alexandrian astronomer must have puzzled with the rest. 

Pondering over the various " phases " which the moon 
presents, it presently came to him that the extent of the moon's 
surface visible to us depends on the direction of the source of 
illumination — that is, the sun. So, as the moon swings in its 
circle, it will reach its first ** quarter '' in a little shorter time 
than it passes from this to the second " quarter," or full moon. 
This is clear from a moment's consideration ; since the moon 
shines by the light of the sun, then when its disk is, to our eyes, 
just cut in two, it is at right angles to an observer on the earth, 
as the figure describes : — 




Fig, 8. 

Now, unless the sun be at an infinite distance from both the 
earth and the moon, it is clear that the time of passage from a 
new moon at N to its first " quarter " at D must be a little less 
than through a full quarter of its orbit, i.e. to H ; so the time 
from the first quarter will be a little longer to a full moon at F 
by the length of the arc H D. It is perfectly easy to time the 



90 THE WORLD MACHINE 

moon*s revolution and its phases. Aristarchus did this and 
believed that he found the first quarter twelve hours shorter 
than the second. To satisfy this result it was a simple matter 
to7compute that the line from E to S — that is, from the earth 
to the sun — must be about eighteen or twenty times the length 
of the line from the earth to the moon. 

Here, then, was a measure of the distance of the sun ! But 
was there any certainty that it was right ? Was there any 
way to check it, to confirm it ? 

It is not very difiicult to see that if, at its first " quarter," 
the face of the moon appears to us just cut in two, the moon 
forms with the earth and the sun a right-angled triangle, such 
as S D E in the figure. It is then only needful to measure the 
angle at E — that is, the angle subtended by the moon and sun 
— to be able to draw this triangle in the right proportions. This 
would give the distance of the sun in terms of the distance of 
the moon. 

All this seems simple enough on paper ; but of an afternoon 
when the sun is setting and the moon is in the sky, it is worth 
a moment's thinking over as to whether such an idea would 
ever have come to you. Note, too, that the angle between the 
moon and the sun is very nearly a right angle, so that the 
smallest error will have enormous consequences. Consider how 
difficult it is to tell just when we see exactly half the moon. 
One wiU think less then that Aristarchus failed than of the 
noble mind which could work out such an idea. 

The Alexandrian's measure of the angle was nearly three 
degrees too small ; his reckoning was out by the xliyth part 
of a circle. It is only fair to add this has been computed from 
other data ; the angle is almost as difficult to measure in our 
day as in his. So the line opposite this angle was about twenty 
times too short. It is evident that his error lay in fixing the 
moment when the moon was at right angles ; for the time of 
passage to the first and second quarter was wrong in exactly 
the same proportion. Aristarchus reckoned this difference at 
twelve hours ; in reality it is on the average only thirty-six 
minutes. He was right in his theory ; his errors lay beyond 
his powers to control. With his resources we could do no 
better now. 

But attend to the curious consequences. Involved in the 
same initial mistake, the impossibility of fixing the exact moment 



DISTANCE AND GRANDEUR OF THE SUN 91 

of the dichotomy of the moon, the one result was confirmed 
by the other, though the two seemed reached by wholly inde- 
pendent means. By yet more singular mischance, a third 
method came to the support of the other two. 

This third means lay in a consideration of the size of the 
conical shadow cast by the earth and the time it takes for the 
moon to pass through it during an eclipse. Whether this 
idea was present to the same amazing brain from which had 
sprung the others, we do not know. It must have been very 
early perceived that in this shadow cone was some sort of a 
clue ; Aristotle had studied it with attention, and he was not 
eminent either as an astronomer or a mathematician. Aris- 
tarchus had certainly given it a great deal of thought, for he 
had made a measure of it and set its diameter, which is not 
very far from the truth. It is certain that he had some method 
by which he estimated the relative diameter of the sun and 
earth, as we shall see ; and the problem could have been worked 
out in this rough way : — 

Knowing the size of the earth, and the size and distance 
of the moon, we may note, during the total occultations of the 
moon, the maximum time elapsed from the moment the edge 
of the moon touches the earth's shadow to the moment it begins 
to emerge. This will enable us to construct a figure showing 
the slant of the conical shadow of the earth, thus : — 









^^— — — — -^^ 


h=^ 


■rk— 


—p^ 


""x — 


^^I^^-^^^^ 


> 


"x 




W 


r^C^^^ ( 


c 


\ 






^^^>^ I 


3 


■~\^ 


^ 


^ 


---IIliA^ 





Fig. 



On the other hand, during an eclipse of the sun, the moon 
on the average just about covers the sun's disk. That is, to 
an observer on the earth at a, the sun and moon during a total 
eclipse of the sun subtend, on the average, one and the same 
angle, B a C or D a F. So, one has merely to prolong the lines 



92 THE WORLD MACHINE 

of the earth's shadow, G I H J, and the hnes, aBaC, until 
the two meet as at D and F, to have the figure we have drawn. 
Knowing the distance from the earth to the moon, one could 
measure the distance to the sun with a foot-rule. 

Did Aristarchus do it ? Possibly not. The device is not 
in his treatise " On the Distance and Size of the Sun and Moon." 
It is likely that it was a development of the next generation or so. 

Living in that same wonderful day was another giant, 
ApoUonius of Perga, styled " the great geometer." His was 
the glory, 'twas said, to have applied geometry to the problem 
of the heavens. Evidently by this was meant the higher 
geometry, for, as we have seen, Bion and Aristarchus and 
Eratosthenes and many another had already given good account 
of themselves in the use of geometrical methods. Apollonius 
developed the theory of conic sections, and introduced the idea 
of epicycles as an explanation of the motion of the planets. 
This latter idea was borrowed by Hipparchus, " greatest ob- 
serving astronomer of antiquity," and it was doubtless the 
example of Apollonius which led him to the discovery of the 
idea of parallax usually attributed to him. It was doubtful, 
though, if he was the actual discoverer. The observation that 
the stars, like other objects, change in their apparent position 
under different points of view, must have been almost as old 
as astronomy, and a geometrical method for taking advantage 
of this must have been found very early. Be this as it may, 
the problem of the shadow cone, as is clear from the pages of 
Ptolemy,^ had been worked out by Hipparchus, apparently 
with great precision, but with the strange result of confirming 
the calculations of Aristarchus. He, too, found the distance of 
the sun about twenty times that of the moon, or from 1379 ^o 
1472 half diameters of our globe. Ptolemy, a couple of centu- 
ries later, tries his hand at the matter, but with no better success 
indeed, he reduces the distance to 1210 such half diameters. 

But with three distinct methods leading identically to the 
same result, there could now be little question of their truth. 
There seems indeed to have been no question for another 
seventeen centuries, and until Galileo and the telescope had 
come. Hipparchus' method — it is generally so styled — is re- 
produced, with new proofs, but similar estimates, in the De 
Revolutionihus of Coppernicus, a.d. 1543. 

1 Almagest, Lib. V. chap. xiv. xv. 



DISTANCE AND GRANDEUR OF THE SUN 93 

The theorem of Hipparchus gave not merely the relative 
but also the absolute measures of the solar and lunar distances, 
hence a direct measure of their size. Cleomedes ^ tells us that 
Hipparchus computed the sun's bulk at 150 times that of the 
earth ; Ptolemy made it 170 times. But Aristarchus, by what 
method he does not state, figured the diameter of the sun at 
between six and seven times that of the earth, hence about 
three hundred times its bulk. He sets the moon's diameter 
at one-third that of the earth — an error of but one-twelfth ; 
admirable, if yet imperfect approximations. The march of 
the mind had begun! 

Yet was this the nearest approach which the ancients made 
to the truth ? There is, in an oddly- jumbled work. Opinions 
of Philosophers, attributed, with slight probability, to familiar 
old Plutarch, a paragraph which says that Eratosthenes had 
engaged the same problem. True to his love of concrete 
measures, he gives the distance of the moon at 780,000 stadia, 
of the sun at 804,000,000 stadia. Marvellous prevision of the 
truth ! For though he makes the distance of the moon only 
about twenty earth radii — too small by two-thirds of the reaUty 
— his figure makes the sun distant 20,000 radii, which, as nearly 
as we may estimate the stadium, was practically the distance 
that, after three centuries of patient investigation with micro- 
meters and heliometers, is set down as the reahty. \ What was 
his device ? how did he guess so wonderfully ? We have no 
mortal idea. Perchance in some buried villa at Herculaneum, 
or elsewhere, a papyrus may exist which may one day tell us. 
Until then we have not so much as a conjecture. 

The estimates of Eratosthenes are somewhat vitiated by 
a remark we find in Macrobius,^ that he gave the diameter of 
the sun at about twenty-seven times that of our earth. His 
great predecessor, Aristarchus, had already fixed the visual 
diameter of the sun at half a degree, which required that its 
diameter should be about xy-th of its distance ; this, on the 
figures of Eratosthenes would have made the sun at least 
ninety times the earth's diameter, or 700,000 times its bulk. 
But Macrobius came in the fifth century a.d., and it may be 
that his remark is an error. True, the figures of Eratosthenes 

1 De Mundo, Lib. I. chap. i. 

2 Somnium Scipionis, Lib. I. chap. xx. 



94 THE WORLD MACHINE 

make the distance of the sun a thousand times that of the moon, 
an estimate two and a half times too great ; but in the face 
of his predecessor's figure of twenty times what a subUme and 
daring error ! 

It is with a deepening interest, bordering even upon amaze- 
ment, that we find yet another great investigator of antiquity 
announcing similar but quite distinct estimates. This was 
Poseidonius, the teacher of Cicero and of Pompey, one of the 
most contradictory of characters, now seeming but a merest 
polymath, now one of the most acute and original thinkers 
of that ancient day. We have already noted that his measure 
of the earth, adopted by Ptolemy, was the sustenance of 
Columbus. He had closely studied the refraction of light, 
and gives us a really wonderful calculation as to the height 
of the earth's atmosphere. In the pages of Cleomedes we 
learn that he equally attempted to estabUsh the distance of 
the stars. He puts the moon at two million stadia away, the 
sun at five hundred million ! This, on his earlier estimate of 
the earth's diameter, would place the moon at fifty- two radii 
of the earth, which would be nearer than the computations 
of Hipparchus. It would make the sun's distance 13,000 radii. 

If we take his later figure (180,000 stadia), the distance 
would become 17,400 radii, an estimate which, considering the 
necessarily wide limits of error, does not differ greatly from 
that of Eratosthenes, and equally little from the truth. Com- 
pare it with the thirteen hundred radii of his forerunners ! 
Compare it with the notions of Epicurus, almost his contem- 
porary, a very wise and large-minded man in his way, who yet 
believed that the sun might be a body two feet across ! 

By what means Poseidonius reached these astonishing com- 
putations, what instruments he had, we do not know, or 
whether his method was the same as that of Eratosthenes. 
His own works have perished, though those of his friend Cicero 
have survived ; and Cleomedes, who has preserved his figures, 
is silent. By means of a clepsydra, or water-clock, he had 
computed the sun's disk at a little over twenty-eight minutes 
of arc, whence he calculated the actual diameter at four million 
stadia, or seventy times the diameter of the earth. Consider 
his age, and you will realise how intrepidly he followed whither- 
soever his calculations carried, even to such unbelievable con- 



DISTANCE AND GRANDEUR OF THE SUN 95 

elusions as this. In the faee of such consistent results it is 
with difficulty that we can credit the statement that he regarded 
the moon as a body larger than the earth. The report is the 
more incredible since he had so closely computed its distance, 
and since its visual diameter is so readily measurable. On the 
other hand, his computation as to the height of the earth's 
atmosphere, the first we know of, would command respectful 
attention for any physical investigation he might make. 

But for either of these estimates, which reached so singularly 
near the truth, what sort of accuracy may we presuppose ? 
What idea can we gain of their value ? 

The large armils erected at Alexandria for Eratosthenes by 
the enlightened Ptolemy Euergetes had a scale, as we know, 
divided down to the sixth of a degree. A moment's considera- 
tion suffices to show that, to be of any value for stellar measure- 
ment, they must have been at least fifteen or twenty feet in 
diameter. They were doubtless made with exceeding accuracy, 
for some of the observations made with them have been of 
value in verifying the conclusions of modern astronomers. Pro- 
bably they were better instruments than any known in 
Christendom until Tycho's day. But even with these they 
could make but rather rough approximations. From a careful 
discussion of the evidence, Bailly ^ concludes that the accuracy 
of the ancients did not surpass five minutes of arc, or one- 
twelfth of a degree. The parallax of the sun, as we know now, 
is less than ten seconds of arc, or not much more than one- 
fiftieth of the limit within which these giants of the past could 
be sure. How then could they guess so well ? 

Baffled by difficulties, the ingenuity of man will sometimes 
turn in unexpected ways. The ancients may have found a 
path that is lost to us. We cannot say. What we know is 
the sun's parallax could have been measured correctly by no 
instrument then known. 

Galileo, with his telescope, sought it in vain. All he could 
know was that it was unobservably smaU, and the sun therefore 
almost infinitely far away. It was not until after twenty-three- 
year-old William Gascoigne, who fell at Marston Moor, had 
slipped a wire-netting across the focus of the telescope, that 
the observation was possible. Galileo, Descartes, Kepler, all 
were dead when it had, at last, in 1670, been made. 
1 Histoire de V Astronomie Moderne, i. 457. 



96 THE WORLD MACHINE 

It revealed, as we know, that the distance and therefore 
the diameter of the sun was not nineteen but four hundred times 
that of the moon. But what did it matter ? Even at nineteen 
times, the sun must be distant from the earth not less than 
five million miles ; it must be a body not less than 50,000 miles 
thick, or seven times the diameter of our vast globe. Who 
could believe it then ? How many dwellers upon this earth 
truly realise it now ? 

And let your fancy linger for a moment over this singular 
fact of history : a space of three centuries separates us from 
the invention of the telescope, the microscope, the thermometer, 
the air-pump, the first electrical machine ; from the days when 
the Pilgrims landed in America, when the plays of Shakespeare 
were first acted in London, and when Bruno was burned in the 
flower-market of Rome. 

At a space of three centuries before the first Christian had 
knocked at the Roman gates, before the first Caesar had 
been crowned, and when Carthage was still mistress of the 
seas, the astronomers of Alexandria had in their possession at 
least a correct relative knowledge of the bodies of the solar 
system. 

Was there any thinker among them to go further, and 
seek to unravel the tangle of their apparent motions, to 
fix the common centre of these motions, and set this solid 
seeming earth for ever spinning 

" Down the ringing grooves of change " ? 



CHAPTER VIII 

THE TURNING OF THE EARTH: THE 
FIXITY OF THE SKY 



For Plato brings in the Egyptian priest, saying to Solon : " You 
Grecians are ever children, having no knowledge of antiquity, nor 
antiquity of knowledge." 

Bacon, Advancement of Learning. 



History, at least in its state of ideal perfection, is a compound of 
poetry and philosophy. 

Macaulay, Essay on Hallam. 



CHAPTER VIII 

THE TURNING OF THE EARTH: THE FIXITY 
OF THE SKY 

We seem to go through the world nowadays with eyes upon the 
ground. We are no longer interested in the pageant of the 
sky. The shows of earth enchain us. City streets are full of 
a restless life, and when, grown weary of the stir and din, we 
take flight to the country, it is the green of the fields, the 
splendour of the sun, we see. The vivid lighting of the cities 
hides the stars, and on the lonely hill-tops the patient shepherds 
no longer guard the night. 

In the olden days, on Mesopotamian plains, or along the 
untroubled current of the Nile, life fared strangely otherwise. 
There were cities, true ; and the days of the eager and restless 
Athenians, the gay and sceptical Alexandrians, the future St. 
Augustine in the arms of the frail beauties of Carthage, differed 
little, doubtless, from our own. But the nights were warm ; in 
those cloudless lands the stars blaze and bum like carbuncles, 
and are full of that mystic fascination from which astrology 
was born. To the watchers of the flocks they were a theatre, 
with an ever shifting scene and a nightly change of bill. 

How intently they must have studied the motley crowd of 
lights that filled the stage, for presently groups of stars took 
on names and shapes ; there were Great Bears and Little, 
Fishes and Swans, Centaurs and Dragons and Scorpions, Archers 
and Charioteers. Hercules, turned a god, showed his form 
nightly to mortals, and through the depths of the blue, Bootes 
drove with his dog. The intense and realistic imagination 
which we observe in children's play, and which the greater 
poets, discoverers, and men of science never lose, finds its 
counterpart in the fancies of those days, when the thoughtfuUest 
of men looked up at the spectacle of the world with the eyes 
of a child. 

Nightly they saw the constellations, as they named them, 

99 



loo THE WORLD MACHINE 

wheel through the dusky vaiilt ; nightly they watched the 
planets come and go, the moon show crescent and then wane ; 
and through the changing seasons saw the heavens change, some 
groups to drop beneath the horizon's edge for a space, while 
others came in view. How intimate their feelings must have 
grown for all these clusters which had to them a name, a myth, 
and a function in the births and deaths of men. Their legends 
of the lost Pleiad reveal how closely they observed, and with 
what poetical felicity their nascent science was robed. It must 
have been all very real to them, and despite their crude fancies, 
their groundless imaginings, their mythopoetics, I think in some 
ways they must have been nearer to the Wonder than the 
theatre-goers of now, who glance occasionally at the sky to 
exclaim its beauty, as they hasten from the shut-up playhouse 
of puppets and tinsel to their suppers or to bed. 

Doubtless the earliest of these figure-groups observed of the 
ancients was the striking arrangement of seven stars which out- 
lines so exactly the shape of a dipper and its handle. Known 
to them was the constellation of the Great Bear ; to our English 
speech as Charles's Wain, there are probably very few of even 
the most indifferent eyes who have not noticed its curious shift 
of position through the night. Seen in the early evening when 
the stars first emerge, the bowl of the dipper may be upright, 
and could be filled to the brim. As midnight peals, and the 
curtain falls and we stumble out into the hubbub of the street 
with the strains of '' Tristan " still throbbing through dazed 
and drunken senses, the group has been displaced and raised, 
and the bowl would now spill its contents ; but still the two 
outermost stars which form the bowl point steadily toward a 
gleam of light that, while all things else in the heavens change, 
does not seem to stir. At a yet later hour, when from some 
function the carriages roll homeward through the silent avenues, 
the dipper is seen to lie still higher in the sky and has turned 
its bowl downwards. Yet the two pointer stars still indicate 
unerringly the centre, round which the whole group seems to 
revolve. 

Studying other groups in the same region, it came to the 
early observers that they, too, seemed to describe an orbit 
round this central star, sweeping through larger and larger 
circles as they were more and more distant from this unmoving 
point. It was all as if the heavens formed a vast and measure- 



THE TURNING OF THE EARTH loi 

less sphere, with the stars set in its surface, and that the whole 
sphere was wheeling round an invisible axis of which this one 
fixed star was the extremity. 

It was from such a mental image that the Greeks gave to this 
radial point of the skies their word for a pivot, ttwAws — and so 
we have Polaris, our pole-star. All this must have been noted 
very anciently, for in the construction of his pyramid, from 
four to six thousand years ago, Cheops had, as we have seen, 
oriented his colossal tomb towards the pivot of the heavens of 
his day. 

Later on, when the idea of the globular form of the earth 
grew into acceptance, among astronomers at least, and the 
beginnings of a climatology and geography were made, they 
came in their poetical way to dress this globe in " zones," or 
girdles ; the circle described by the sun at its northern solstice 
was the boundary of one ; that described at the southern 
station, of the other ; and as it was at the edges of this belt 
that the sun seemed to turn back, they named the boundary 
line the " tropics," the same as our word trope, or turn. Mid- 
way between the two, they noted that the sun in its revolution 
described a great circle of this globe, and when it was at this 
point, the days and nights were equal all over the earth ; 
whence they gave this great circle the name of the equant, or 
equator. It must have puzzled the early observers vastly to 
know why the sun should thus shift up and down in the sky. 
Their puzzling must have deepened when they made a further 
step. The planes, they noted, formed by these circles, were 
parallel one to the other, and a line drawn through their centres, 
and perpendicular to them, passed through the centre of the 
earth ; projected into space, it pointed straight to the pole- 
star. In a word, it seemed as if the earth had an axis like the 
heavens, and this seeming axis of the earth and the seeming 
axis of the skies were one. Here was something to ponder. 

Of course, so long as they had no mortal idea of the distance 
of the sun and stars, they had no trouble in believing that it 
was the sun and the crystal sphere of the stars which moved. 
But very early some penetrating mind must have struck in with 
the thought that this motion might be explained another way — 
that the daily revolution of the sun, the nightly wheeling of the 
stars, was the effect of the slow turning of the earth, and that 
the sphere of the sky stands still. Just as on a very large 



102 THE WORLD MACHINE 

vessel, we sometimes have the illusion that it is the shore and 
docks which are going by, so it might be that we have the same 
illusion regarding the stability of the earth. 

By common credit, Pythagoras is held to have been the first 
to have taught such a doctrine ; but it is not very clear that 
he did ; it is many times certain that he was not the first. 
Pythagoras was a product of that highly intelligent society 
which rose among the Greek colonies in southern Italy, while 
Athens was still the home of marauding pirates. He travelled 
widely, and it was doubtless in Egypt that he heard of this 
monstrous paradox of the earth's motion. He seems to have 
imbibed the notions of the old priestly caste that science and 
knowledge were to be guarded by a secret band and to be com- 
municated only to the initiate. 

Among his disciples it is evident that the paradox was 
bruited openly, so that by the time of Plato and Aristotle, it 
is a matter of general debate. Aristotle, who cuts rather a 
sorry figure as a thinker, had no hesitations ; he chose a fixed 
and immovable earth. But Plato, who had made a journey 
to Italy to learn of the new doctrine, seems in his old age to have 
wavered, and thought perhaps he had made a mistake in taking 
the same view. But it was on purely sentimental grounds, from 
esthetic considerations, that he wavered ; reason or fact did 
not disturb the Platonic soul. Indeed, to read the monstrous 
wish-wash which passed for logical argument in those days, and 
for a thousand years thereafter, one might now readily imagine 
that since that day the processes of reasoning had completely 
changed, and hence might completely change again, in another 
millennium or so. It is a curious and disturbing thought ; but 
we need not be agitated. Happily we know there were among 
the Greeks thinkers of the highest order, men of trained and 
logical minds, like Democritus and Anaxagoras, Euclid and 
Aristarchus, whose conceptions, so far as they got, differ but 
little from our own ; and we may conclude that, with its Platos 
and Aristotles, Greece was then, as our own time now, full of 
vain babblers, imposing upon a generation, in Carlylean defini- 
tion — " chiefly fools." 

With the advent of mechanical conceptions, this abracadabra 
which passed for philosophy and sense ceased to satisfy men's 
minds. They began to scrutinise more closely. 

It is clear from the work of Copper nicus, which probably 



THE TURNING OF THE EARTH 103 

contains little in the way of general considerations which had 
not been eagerly discussed by the Greeks, that one especial 
argument against the revolution of the fixed stars was the 
frightful speed at which they would have to travel in order 
to complete the circle of the heavens in twenty-four hours. 
The sling in those days was a common weapon ; and they would 
be led to consider that while it is easy to whirl an object about 
on, say, a foot leash, at a high rate, this becomes increasingly 
difficult as the leash is lengthened. So also with a little wheel 
and a big one. 

If, therefore, it seemed preposterous that so great a thing as 
the earth could turn, it was still more difficult to imagine the 
flight through space of other large bodies, like the sun, in an 
enormously larger orbit. This difficulty must have become 
of increasing moment, as it became clear that the sun was 
even larger than the earth, and hence almost inconceivably 
distant. 

But if, as is abundantly attested by various fragments, there 
were close reasoners like Philolaus of Crotona, Hicetas of 
Syracuse, Heraclides of Pontus and others, who could maintain 
the daily revolution of the earth, there were still difficulties 
enough. The turning of the earth explained with exquisite 
simplicity the apparent revolution of the heavens ; it did not 
clear up the curious shift of the sun with the seasons. This 
shift was double, first with reference to the circle the sun 
describes in the heavens each day, with which the length of 
the day seemed bound up ; and second, with reference to the 
fixed stars. 

Why should the sun seem thus to wobble in the sky ? why 
should the days be nearly twice as long as the nights in summer, 
and in the winter hardly half ? If the earth be in reality 
a revolving globe, a vast barrel-churn, one might go a step 
further and suppose that, for some reason or other, it was 
wobbling on its axis as well — back and forth, swaying six months 
one way and six months the other. This would explain the 
change in the sun's apparent position, the change of days, and 
of seasons too. But if it was a mental wrench to try to think 
of a whirling earth, it was sheer deracination to propose an 
earth that not only whirled, but in whirling swayed! The 
mind grew vertiginous over the abyss of such a thought. Turn 
it might, upon an axis that was fixed — the idea was even 



104 THE WORLD MACHINE 

plausible. But turn upon an axis that seemed to lurch — 
who was there to venture on so outrageous a notion ? What, 
then, im Teufelsnamen, did this axis rest on ? It cannot sustain 
the earth if it is supported on nothing. Moreover, on a second 
thought, the axis did not appear to lurch. Always, in season 
and out, it pointed steadily toward that mystic pivotal star of 
the north. The explanation must lie elsewhere. 

Perchance not alone the earth but the sun moved too ! So 
it actually seemed, for watching its risings and its settings from 
month to month, the ancients very early noted that it came 
up amid one group of stars at one time, and in a different one 
a little later. From one end of the year to the other it seemed to 
traverse a sort of belt, which they duly decorated with names 
and fantastic shapes. 

Taking the year at roughly twelve lunations, they divided 
the belt into twelve signs, put a lobster in one, a goat in another, 
a virgin in a third, fishes in a fourth, a bull next, and so on. 
The various animals were ranged in a circle, much as the cages 
in a circus tent, and the whole menagerie they called the Zodiac, 
or " circle of the animals." In a given season the sun was said 
to rise, or set, in Aries or Pisces or Virgo, and due and dire things 
depended thereon. 

There were but two ways in which all these puzzling appear- 
ances could be explained ; two, and only two. Either the sun 
goes round the earth as a centre each year, in a circle that is 
inclined at a considerable angle to the plane of the earth's 
equator, or else the earth goes round the sun in the same sort 
of a plane — in brief, has a dual motion. SmaU wonder that 
common folk shook their heads when the learned astronomers 
began to indulge such speculations as this. 

But the world and the wonder of it was very new ; and 
the new science of geometrical constructions seemed to do such 
wonderful things. Starting from the simplest proposition, which 
even a child could understand, the geometer carried the mind 
along from theorem to theorem, until the solid earth seemed to 
have been left far behind ; yet no link of proof seemed lacking ; 
all was rigidly enchained. It was thus-wise that men were 
able to get away from the bondage of appearances, and by a 
process of abstraction, reach beneath the surface to the inner 
core of things. So, the history of these ancient speculations 
being lost, we may imagine some among them drawing a circle, 



THE TURNING OF THE EARTH 105 

setting the sun at the centre, the earth in an orbit about it, 
and the ** circle of the animals " still outside of that. Let us 
do the same. 

It is easy enough to see that if the earth is on one side of 
the sun, as at E, and its daily revolution makes the sun appear 
to " rise," the sun will be seen to come up in the direction of 
the group of stars which lie against the face of the sky opposite, 
say the constellation of Leo. When the earth has swept round 
a quarter of a turn, at E^, then the sun will seem to rise in Aries, 
and so on around the whole circle. All this is simple enough 
and satisfactory too, in a way ; but there are many points to 
tax credulity. For example, one must suppose that, as the 



^VLe^ 




corrv 



Fig. 10. 

earth's axis is always pointed in the direction of the pole-star, 
it sweeps round the sun always tilted on its side, and always at 
the same tilt. But this would explain the change of the length 
of days. If the earth on one side of the sun leaned a little 
so that one pole would be in darkness all the time, then if it 
kept leaning the same way, when it got around to the opposite 
side of the circle, this dark pole would be constantly in the 
sunlight. And this is exactly what happens. So the seeming 
difficulty becomes an added proof. 

But what a tipsy and disconcerting vision it summons ! — 
this giant earth, careening about the sun in a plane, but 
always turned partly on its side, as a ship buoy often floats 
upon the surface of the water. Yet, how much it explains ; 
how it simplifies ! What must have been the glow of pleasure 
to him who first reasoned it out ! 



io6 THE WORLD MACHINE 

" Felix qui potuit rerum cognoscere causas ! " 

So Virgil sings ; life has no purer joy. Yet whosoever was 
this first, the lips of history are mute. Some king's " magician," 
or soothsayer of the Nile, perhaps ; no mighty cenotaphs im- 
mortalise his name ; not for such as he do a hundred thousand 
burdened slaves sweat and grunt through thirty years to rear 
a tomb. 

For that matter, there may have been no one. Great con- 
ceptions, great discoveries, have no Minervan birth. So, here 
and there among the old Greeks, we find men who seem to have 
caught sight of the idea, but did not " see it clearly and see it 
whole." Thus old Hicetas of Sjnracuse, or Nicetas, as Cicero 
calls him — Cicero's account, doubtless, was not very accurate, 
for Cicero was a literary man ; it may quite misrepresent. But 
Hicetas, he says, pictured the earth as " turning and twisting 
on its axis while all else in the heavens stands still." Quaint 
and ingenious thought. In another century a great Alexandrian 
wiU take out the twist, and thus, away back there, work out in 
all its essentials our modern welt-anschauung. 

But the proposal to give the earth not only a rotatory but 
a translatory motion as well, drove against a simple but very 
formidable obstacle. That was the dislocation which two 
bodies — our two peaks from the Matterhorn, for example — 
seem to undergo when we change our point of view. If the 
sun be at an enormous distance from the earth, and the earth 
goes round it, then from one side of the circle to the other we 
shall view the stars from two enormously separated points. 
Some of the stars must appear to shift their position one to 
another if this be true. 

No one could find the slightest change in the stellar sphere. 
Alone the sun and planets moved. 

True if one could think, with Eudoxus, that the stars were 
set in the face of a solid sphere, so all would be at an equal dis- 
tance, there, would be no difficulty. But it was clear that the 
planets were widely ranged in space ; the eclipses left no doubt 
of that; their brilliancy suggested the same. There was the 
same varied brilliance among the unmoving stars ; they differed 
from the almost planet's glow of Sirius and Arcturus to the 
faintest gleams. 

There was one escape, and one alone. That was to conceive 
the fixed stars as so remote from all mundane relations that, 



THE TURNING OF THE EARTH 107 

compared with this, even the distance of the sun was as nothing. 
But so doing seemed to loose the earth from its moorings, and 
toss it hke a fragile bark upon the wastes of a boundless sea. 
It was to view the sun and earth and its vast orbit as but a 
point in the unending marches of the sky. Lost in such reverie 
of the infinite, the imagination reels in drunken sublimity ; 
the ways of space became a welter of whirling specks ; the 
aimless motions of a cloud of insects, the image of the handi- 
work of God. Staled by custom, by constant iteration, we 
have become a little steadied to the view. But to what som- 
nambulist of space did it come first ? Is there any mind in 
Hellas to rise to such an outlook on the world ? 
What said Aristarchus ? 



CHAPTER IX 

THE FLYING EARTH: THE FIXITY OF 
THE SUN 



The human mind has been young ; it was poor, but it has become 
rich ; it was ignorant of what it now knows. Ideas have been 
successively gathered together, heaped up ; they have mutually 
engendered each other, the one has led to another. It remains 
therefore merely to rediscover this succession, to begin with the 
earliest ideas ; the path is traced out ; it is a journey that one 
may make again because it has already been made ; the individual 
may now cover in the course of some hours' reading an extent of 
knowledge which it has cost the race long centuries to acquire. 

Bailly, Histoire de I'Astronomie Moderne. 



CHAPTER IX 
THE FLYING EARTH: THE FIXITY OF THE SUN 

From out the wrecks of time not much of the learning of the 
ancients has been saved. Goth and Hun, priestly zealots and 
fanatical conquerors, left little, and on what they left the 
worms have fed. The library in Alexandria was, all things 
considered, certainly the most wonderful gathering of books 
which ever existed — 700,000 volumes, copied by hand. It 
would represent a hundred times the value of the great libraries 
now existing. We do not know that a single volume of it 
remains. From the torch of Ccesar's legions, and the wild rabble 
of Christians under Theophilus who sacked and burned it four 
hundred years after, not much was spared to give body to 'the 
myth of the conquering Omar who came four centuries later still. 

So of the works of Aristarchus there has come down only 
the thin volume wherein he sets forth the measures of the sun 
and moon. It is to another small volume, four hues at that, 
that we owe our knowledge of what views he held of the world 
he had thus surveyed. This was that strange Arenarius, or 
" sand-reckoner," wherein Archimedes attempts to show how 
it is possible to express in figures the number of grains of sand 
that the whole celestial sphere might hold were it filled full. 
It is the play of an intellectual frestidigitateiir, a juggler who 
takes numbers for balls to toss and the universe for his stage. 
He tells us that he will not take for the radius of the steUar 
sphere merely the distance of the sun from the earth, " as most 
of the astronomers do " ; he wiU show that he may cope even 
with the ideas of Aristarchus. And so we chance to know 
what this celebrated Aristarchus taught — that the distance of 
the stars is incommensurable to men. 

It is easy to think that these ideas of the ancients were 
merely fancies ; that they thought over things a little, then 
hazarded a guess ; and guessing much and often they might 



112 THE WORLD MACHINE 

sometimes guess aright. Listen then to what Archimedes 
says : — 

" Aristarchus of Samos, confuting the hypotheses of the 
astronomers, concludes that the world is yet many times greater 
than the estimate we have just given (about 1300 earth radii). 
He supposes indeed that the stars, like the sun, remain im- 
mobile ; that the earth revolves, following the circumference 
of a circle, round the sun as a centre, and that the sphere of 
the fixed stars, having this same sun for a centre, is of such 
vastness that the circle in which the earth moves, has to the 
distance of the fixed stars, the same proportions as the centre 
of a sphere to its surface^" — that is to say, a circle millions of 
miles across, looked at from the fixed stars, would be but a 
point in immensity ! 

This was in the third century B.C. At the beginning of the 
seventeenth century a.d., when Tycho Brahe, Kepler, Galileo, 
and a host of others, were debating the theory of Coppernicus, 
the objection brought by Tycho, as we have already noted, 
was that if the earth does revolve, then the stars would shift 
a little in their relative positions. That point Galileo could 
not meet. Though he sought eagerly to find a parallax, if 
only for a single star, he sought in vain. It was not until some 
seventy years ago that such a shift of position was conclusively 
demonstrated ; and with it the last link set in the chain of 
proof which establishes the Coppernican theory. Two thousand 
years before Tycho, Aristarchus had met this objection in the 
only way it could be met, and had divined the truth. 

He had divined, had guessed, rather than demonstrated. 
Was there, then, any way to prove this idea of the distance 
of the fixed stars ? 

In the opening of Coppernicus' work there is to be found a 
theorem of amazing simplicity which does offer this proof. But 
it did not originate with the Polish astronomer ; he copies it 
from the Almagest of Ptolemy ; it is in the treatise of Cleomedes ; 
where Cleomedes got it we do not know. Both appear to have 
been chiefly compilers. Moreover, the idea is such a one as 
might readily have occurred to the earliest of those who had de- 
monstrated that the earth is round. It was doubtless very old. 

The chapter in Coppernicus is entitled, " Considerations on 
the Immeasurable Extent of the Heavens in Comparison with 
the Size of the Earth," and his theorem is this : — 



THE FLYING EARTH 113 

At any given moment of time the horizon of the earth divides 
the sphere of the heavens exactly in two, and this is true, not 
merely through each twenty-four hours, but throughout the 
year. It follows, therefore, that neither the great mass of the 
earth nor its distance from the middle point of the world occasions 
the slightest difference in this continuous bisection of the 
heavens. Did either the one or the other enter into considera- 
tion, we should see always less than half the sky. Test it 
any moment and you will see that this is never the case. Long 
observation had taught the ancients to fix, with a precision 
stiU of great value, the exact position of the different constella- 
tions of the zodiac. They knew, for example, the beginning 
of the sign of Capricorn was precisely opposite, in the zodiacal 
circle, to that of the Crab. Take now one of their old diopters 
or horoscopes, or sight across a water-level, and you see that 
at the moment the Crab '' rises," Capricorn " sets " ; a line 
from one to the other is a diameter of the zodiacal circle, or, 
as we say, of the plane of the ecliptic. Now when the heavens 
have turned about so that we just see Capricorn rising, the 
Crab is just slipping under the opposite horizon. You may 
draw a circle, if you like, just as did Ptolemy or the unnamed 
genius who first worked it out, like this : — 




Fig. II. 

You have now two diameters which cross a common centre, 
and it is easy to show that this centre is likewise the centre 
of the earth. Lines from the surface of the earth and from 
its centre to a common point cannot be the same ; neverthe- 
less, so far as the observation of the stars reveals, they are not 
only parallel, but, on account of the vast distance of the stars, 
one and the same line. The half diameter of the earth, there- 
fore, is, with respect to the distance, an entirely negligible 
quantity. Not merely this, but if you believe, as Aristarchus 
did, that the earth moves round the sun as a centre, and that 

H 



114 THE WORLD MACHINE 

the sun is the true centre of the stellar sphere, then it follows 
that, with respect to the distance of the fixed stars, the diameter 
of the earth's orbit is likewise negligible ; as Coppernicus puts 
it, it is the '' relation of a point to a body, of the finite to the 
infinite." 

This is to all intents the language of Aristarchus, though 
Coppernicus does not quote him either here or elsewhere. 
Whether the Alexandrian knew of this simple demonstration 
of his belief, is buried with his lost treatises. He certainly 
had the idea in all its consequences. We may believe he was, 
in all probability, the first of the human race to see the world 
as it is ; the first adequately to understand what infinitude 
may mean. 

And if this be true, an injustice to history has been done. 
Yielding in no wise the honours that time has paid to that 
patient mind which, in an obscure corner of Poland and through 
forty years of silence, laboured to set the universe in its order, 
the system of the planets, if it bear a name, should transmit 
to posterity not that of Coppernicus but that of his far greater 
predecessor in the gay capital of the Ptolemies. 

If we may trust Sextus Empiricus, and others who make 
mention, Aristarchus founded, in some sense, a school. His 
authority was clearly of the highest, yet in all antiquity he 
seems to have had but one notable follower, Seleucus of Babylon, 
who came perhaps a century later. Archimedes did not seem 
to accept his views ; neither did Eratosthenes, nor the great 
Hipparchus, nor Poseidonius, nor that Ptolemy the astronomer, 
whose luck it was, like Aristotle, and with as little worth, to 
be a standard among men for so many centuries after. What 
was the reason ? 

One may sometimes meet with a curious statement that 
Hipparchus had in his hands a means of demonstrating the 
truth of the Aristarchan theory, but failed to make use of it. 
This lay in his new method of computing the distance of the 
sun and the moon, and in uniting these with Eratosthenes' 
measure of the earth. But as the preceding pages have already 
disclosed, Hipparchus did make use of this method, with the 
singular result of confirming the surprising though inadequate 
results of the Alexandrian astronomer. 

Moreover, we have seen that Aristarchus himself, a century 
or more before, had computed the grandeurs of the sun and the 



THE FLYING EARTH 115 

moon in terms of the earth's measure, demonstrating that the 
diameter of the sun compared with that of the earth is greater 
than 19 : 3 and less than 43 : 6, that is, between six and seven 
times ; he therefore estimated the grandeur of the sun at three 
hundred times that of the earth. And we have the word of 
Aristotle that an approximate measure of the earth had been 
made yet another century before Aristarchus had pointed his 
astrolabes at the Alexandrian sky. It is an error to suppose 
that it was a mere question of geometrical methods or measures 
— of mere dimensions ; for the dimensions were known, at 
least in the right relative proportions, to the founders of the 
two rival systems. 

The difficulty, as the learned Schiaparelli has been at the 
length of an interesting memoir to prove, lay elsewhere. One 
was the invention of a new system, which represented all the 
known facts equally well. That was the theory of epicycles, 
picturing the planets as gyrating through a circular path round 
a circle. This system, worked out in detail by Hipparchus 
from the mathematical developments of Apollonius of Perga, 
was adopted by Ptolemy, and held the field until Tycho Brahe's 
day. And it is curious to reflect that, within the confines of 
pure astronomy, the absolute disproof could not come until 
the establishment of the parallax of the stars, in our own time. 
Even the simplicity of the Coppernican scheme could not prevail 
over it until a new science was born. That was dynamical 
mechanics, the mechanics of motion, unknown to Hipparchus' 
and to Aristarchus' era. Though the one might think it ,absurd 
that about the lesser earth the greater sun should turn, the 
other evidently did not. 

The keen and restless-minded Eratosthenes could conceive 
the sun as a body not three hundred, but twenty thousand 
times the bulk of this globe we live on, set it at eighty or ninety 
millions of miles away, and yet have no difficulty in revolving 
such a colossus round an unmoving earth, once in each twenty- 
four hours. The unthinkable speed it must attain seems to 
have brought no dismay to his mind. He could calculate as 
easily as you and I that this meant a body at least 200,000 
miles in diameter, whizzing through space at the rate of 400,000 
miles per minute, 23,000,000 miles per hour ; and still always 
describing a perfect circle (so far as he could judge) about this 
central speck of earth. 



ii6 THE WORLD MACHINE 

Even so, and even more, Poseidonius. Though he makes 
the sun hardly less distant (50,000,000 of miles) ; though he has 
a truer idea of the sun's immensity than any other man in 
antiquity, fixing it at 400,000 miles, or at near half the reality ; 
though he thus conceives it, apparently, as a body seventy times 
in diameter, therefore three hundred and fifty thousand times 
in volume the earth, and sets its orbit at near ten thousand times 
the earth's circumference ; though he seems the first of physical 
investigators to perceive that the height of the tides is dependent 
upon the positions of the sun and the moon ; not even he can 
find it singular that so vast a thing should move in a rigid 
curve about the earth. It does not seem absurd to him, nor 
to his near contemporary, Cleomedes, though Cleomedes per- 
ceives the truth that our globe is a body so comparatively 
slight that, seen from the distance of the sun, it would appear 
but a point. It does not seem absurd even to the mechanical 
and inventive mind of Archimedes, himself the founder of two 
great branches of mechanical science. 

The failure of the penetrating intellect of the great Syracusan 
to grasp the truth of the Aristarchan conceptions is the more 
amazing from the fact that he was the first, apparently, to 
devise a mechanical representation of the motions of the 
heavenly bodies ; he was the first world-mechanic. The 
planetarium he constructed, the orrery of our day, was the just 
marvel of the ancients. In the Commonwealth of Cicero, there 
is a naive and charming page that is well worth transcribing 
here : — 

" I recollect that Caius Gallus, who was a man of profound 
learning, while he was staying at the house of Marcus Marcellus, 
asked to see a celestial globe which Marcellus* grandfather had 
saved after the capture of Syracuse, from that magnificent and 
opulent city, without bringing to his own house any other 
memorial out of so great a booty ; which I had often heard 
mentioned on account of the great fame of Archimedes. Its 
appearance, however, did not seem to me particularly striking. 
But as soon as Gallus had begun to explain, in a most satis- 
factory manner, the principle of the machine, I felt that the 
Sicilian geometer must have possessed a genius superior to 
anything we usually conceive to belong to our nature. For 
Gallus assured us that the solid globe, made by the same 



THE FLYING EARTH 117 

Archimedes, and deposited by Marcellus in the temple of virtue 
at Rome, was a very ancient invention, and that the first had 
been made originally by Thales of Miletus ; but that the motion 
of the sun and the moon and the five planets, or wandering stars, 
could not be represented by this primitive solid globe ; and 
that in this the invention of Archimedes was admirable, because 
he had calculated how a single revolution should maintain un- 
equal and diversified progressions (of the planets) in dissimilar 
motions. In fact, when Gallus moved this globe, we observed 
that the moon succeeded the sun by as many turns of the wheel 
in the machine as days in the heavens. From whence it resulted 
that the progress of the sun was marked in the heavens, and that 
the moon touched the point where she is obscured by the 
earth's shadow at the instant the sun is at the opposite side." 

The remainder of the passage is lost. But as any one who 
has ever inspected an orrery must know, the construction of 
this highly complex mechanism required not merely an extra- 
ordinary ingenuity, but all that mathematics might teach as 
well. We know, moreover, from many a passage in the works 
of Cicero and elsewhere, that it was the demonstrations of 
Archimedes, rather than of Aristarchus, which spread among 
the enlightened people of that day the doctrine of the vast size 
of the sun, the littleness of the earth. 

We know, too, that even in Archimedes* day, some reflective 
minds had already begun to picture certain of the planets as 
having the sun at the centre of their orbits, rather than the 
earth. Long and thoughtfully had they watched the course 
of the " wanderers," had seen them rise and set like the sun and 
the moon, wax and wane in brilliancy ; observed Venus when 
it casts a shadow, and again when it has shrunk to the size 
of Saturn ; seen Mars blaze out in redness, then shrink away 
to hardly more than a point. That Venus and Mars, Saturn 
and Jupiter were of the same general nature as the moon, had 
long been known. It was clear enough that the moon revolved 
about the earth and not about the sun. This naturally led to 
the idea that all planets did the same ; but it was disturbing 
to see Venus now crossing the face of the sun, now obscured 
by it. And so perchance with Mercury. 

Perhaps the sun, hke the earth, might have its satellites, 
and it was thus, apparently, that Mercury and Venus were 



ii8 THE WORLD MACHINE 

ranged in the scheme of ApoUonius of Perga, he whose ideas 
seem most deeply to have influenced Coppemicus. 

From this, to set the earth among the planets was but a 
step. No, not a step, it was a leap across a chasm, the abyss 
that lay between the old geometric world-conceptions and the 
new. The mind of Aristarchus could make the leap ; Archi- 
medes, ApoUonius, Eratosthenes, Hipparchus, Poseidonius, 
Cleomedes, Ptolemy, and the rest could not. On the other 
side one giant figure stands alone. 

In the planetarium, as constructed by Archimedes, the five 
planets which, in the lack of the telescope, could be known, 
seem to have been placed in their proper order, save in this 
one regard : their orbits centred in the earth. How a man 
with a brain to work out and the cunning hand to build such 
a mechanism could thus stop short, passes understanding. He 
was at once one of the greatest mathematicians and inventive 
geniuses that ever lived. He had in his hands, and was, so 
far as we know, the first actually to employ that happy com- 
bination of the three sciences which have made possible the 
marvellous attainments of modern astronomy. Yet more, his 
studies and discoveries in mechanics were leading him straight 
toward that mechanical explanation of planetary motion which 
immortalised the name of Isaac Newton. He was familiar 
with the problems of the ellipse eighteen centuries before 
Kepler's birth ; the idea of a centre of gravity was his idea ; 
he was even a measurer of the force of gravity. One further 
step and the discoveries of Galileo, and perchance of Kepler 
and of Newton too, might have been perfected before the 
Roman dominion had set heel upon Hellenic culture, and before 
the gospel of an avenging Jehovah had been carried beyond 
the confines of the little country of Palestine to make of truth 
blasphemy. 

It was all so astonishing, they came so near : it may lend 
some helpful insight into the workings of the human mind to 
consider attentively their failure. 



CHAPTER X 

ARCHIMEDES AND THE FIRST IDEAS OF 
GRAVITATION 



First let us examine the earth, whose situation is in the middle 
of the universe — solid, round, and conglobular by its natural 
tendency. 

. . . What is most wonderful is that the world is so durable, and 
so perfectly made for lasting that it is not to be impaired by time ; 
for all its parts tend equally to the centre, and are hound together 
by a sort of chain, which surrounds the elements ; this chain is 
nature, which being diffused through the universe, and performing 
all things with judgment and reason, attracts the extremities to the 
centre. 

If, then, the world is round, and if on that account all its 
parts, being of equal dimensions and relative proportions, mutually 
support and are supported by one another, it must follow that, as 
all the parts incline to the centre (for that is the lowest place of a 
globe), there is nothing whatever which can put a stop to that pro- 
pensity, in the case of such great weights. For the same reason, 
though the sea is higher than the earth, yet because it has the like 
tendency, it is collected everywhere, equally concentres, and never 
overflows, and is never wasted. 

The stars have their revolutions in the sky, and are continued 
by the tendency of all parts towards the centre ; their duration is 
perpetuated by their form and figure, for they are round ; which 
form, as I think has been before observed, is the least liable to 
injury. 

Cicero, Nature of the Gods. 



CHAPTER X 

ARCHIMEDES AND THE FIRST IDEAS OF 
GRAVITATION 

The earth is round, but water flows. Why do not the oceans 
run down hill and spill away into the void ? 

The cause, the " reason," seems so obvious to us now that 
it is a little difficult to realise that this was once a puzzle and 
stumbling-block. Let us go back and consider the problem 
with the earliest of the physiographers. One of Jthese was that 
same Eratosthenes whom we have seen measuring the circum- 
ference of the earth, the tilt of its axis to the plane in which 
the sun revolves ; computing the distance of the sun with 
greater success than any investigator of antiquity ; a giant 
mind, and, moreover, one of those finely trained imaginations 
which seems able to escape the enveloping trammels of accus- 
tomed methods and beliefs, to reach a larger view. But no 
man can shake himself wholly free from the web of his own time ; 
so we find in Strabo such an extraordinary passage as this : — 

" However, so nice a fellow is Eratosthenes, that though he 
professes himself a mathematician, he rejects entirely the dictum 
of Archimedes, who, in his work, On Bodies in Suspension, 
says that all liquids, when left at rest, assume a spherical form, 
having a centre of gravity similar to that of the earth ; a dictum 
which is acknowledged by all who have the slightest pretensions 
to mathematical sagacity. He says that the Mediterranean, 
which, according to his own description, is one entire sea, has 
not the same level even at points quite close to each other ; 
and offers us the authority of engineers for this piece of foUy. 
He tells us that Demetrius intended to cut through the Isthmus 
of Corinth to open a passage for his fleet, but was prevented by 
his engineers, who, having taken measurements, reported that 
the level of the sea at the Gulf of Corinth was higher than the 
opposite side, so that if he cut through the Isthmus, not only 



122 THE WORLD MACHINE 

the coast of ^Egina, but ^gina itself, would be laid completely 
under water." ^ 

And Strabo laughs. Is this Strabo some philosopher of the 
days, say, of Elizabeth or Louis Quatorze, sneering at the 
wisdom of the ancients ? No, somewhat further back — back 
even to the time when they were setting a crown on the head 
of the first Imperator of Rome. And this cheery old Strabo, 
writing his celebrated geography, if we may trust Humboldt, 
when he had passed eighty, goes on to reprobate these ideas 
of the Alexandrian as plain nonsense. These currents in the 
Mediterranean, between ScyUa and Charybdis, and elsewhere, 
which Eratosthenes adduces, are, he says, the effect of the tides ; 
and the tides and their dependence on the rising and the setting 
of the moon, have been sufficiently treated by Poseidonius and 
Athenodorus, so that he does not need to go into the matter. 
So the flat misprisions of his predecessor seem to him simply 
absurd. " Whoever," he exclaims, " imagined the surface of 
the ocean to be on a slope ? For water is not like the earth, 
which, being of a solid nature, is capable of permanent depres- 
sions and risings, but by the force of gravity spreads equally over 
the earth, and assumes that kind of level which Archimedes 
assigned to it ! " 

Thus Strabo, a.d. 25. In Poseidonius, a full century before, 
and in Archimedes, yet another century back of him, we find 
clear enough conceptions that the oceans lie at a general level 
over the surface of a spherical earth, perforce of a power directed 
towards the earth's centre. That gravity draws always to the 
centre, seems to have been present, hazily, in the hazy mind of 
Aristotle ; it was clearly one of the established verities in the 
Alexandrian school a century later. Strabo even makes of it 
an argument for the sphericity of the earth, since " all things 
however distant, tend toward its centre." A weight hung on 
the end of a string is always perpendicular to the plane of the 
horizon, that is, to a tangent to the earth's surface, an5Avhere. 
If the earth is a sphere, it follows that the plumb-line points 
always to the centre of the sphere. 

Bodies falling from no matter what height fall always in the 

same line ; they form a perpendicular to a water level. This 

the ancients knew well. It was as if there is an attractive force, 

acting from the earth's centre. And this force seemed constant, 

1 Strabo, Geography, i. p. 85 ; ed. Bohn. 



THE FIRST IDEAS OF GRAVITATION 123 

it did not diminish, highsoever as they could go ; indeed the 
greater the height from which a body falls, the longer the time 
it is falling, the swifter the speed of the fall. 

Does this force extend then indefinitely up into the sky ? 
What, for example, is the meaning of this curious connection 
which seems to subsist between the moon and the tides, which 
Poseidonius and Seleucus have studied so attentively. Does 
the moon pull the waters of the sea ? And if so, is this pulling 
force between moon and earth reciprocal ? Why, for example, 
does the moon move round the earth in a circle ? Why does 
it not fly off into space ? What holds it ? Is this same 
attractive force, acting towards the earth's centre, constantly 
pulling the moon downwards towards the earth, as an arrow 
shot into the air falls back again when its force is spent ? 

There were surely minds before which this far-reaching con- 
ception floated ; in foremost line that rich, proud Anaxagoras, 
whom Pericles saved from the vengeance of the Athenians for 
his cold disdain of their rabble of gods. Humboldt quotes 
Jacobi as commenting on " the profound consideration of nature 
evinced by Anaxagoras, in whom we read with astonishment a 
passage, that the moon, if its centrifugal force ceased, would 
fall to the earth like a stone from a sHng.*' It was this 
same Anaxagoras who pictured " the ether surrounding the 
earth as a fiery substance which by the power of its rotation 
tears rocks from the earth, inflames them and converts them 
into stars," ^ a curious antithesis of present-day ideas of 
meteorites. It was doubtless in following out his idea that 
Anaxagoras came to regard the sun as a colossal body of red- 
hot iron. 

In Diogenes of Apollonia, in Democritus, in Empedocles, in 
Plato and others, are to be found notions more or less vague, 
of this same force of attraction. " It seems almost to have been 
common property. In Plutarch, in his Life of Lysander, is 
to be found a curious passage regarding faUing stars, " which 
are," he says, " according to the notions of some of the 
physicists, not eruptions of the ethereal fire extinguished in 
the air immediately after their ignition (!), but these meteors 
are rather a faUing of celestial bodies, which, in consequence of 
a certain intermission in the rotatory force, have been hurled 
down." 

1 Plutarch, De Placitis Philosophorum. 



124 THE WORLD MACHINE 

Yet clearer is Simplicius, one of the last of the great 
Alexandrian school, who, in his commentary on Aristotle, attri- 
butes the " non-falling of heavenly bodies " to the fact that 
" the rotatory force predominates over the actual falling force 
or downward attraction." That this was no mere guess, and that 
Simplicius had perfectly definite ideas of the physical fact of 
which he is speaking, is evidenced in his illustration from the 
familiar instance that " water in a phial is not spilled when 
the .movement of rotation is more rapid than the downward 
movement of the water." ^ 

Moreover, it is clear that Aristotle and Hipparchus as well, 
knew of the acceleration of falling bodies, but neither they nor 
any one apparently seems to have thought of the simple expedient 
of measuring the rate of the fall, and hence finding out the rate 
of the acceleration. 

This is the more notable in an observing genius like 
Hipparchus, who, unlike Aristotle, had that exact and measuring 
mind which is essentially the type of the modern creators of 
experimental science. It was Hipparchus who discovered the 
precession of the equinoxes, a fact which required not merely 
the most delicate observations, but a mind intensely alive. He 
was a mathematician, and he constructed the first table of 
chords. Apparently it was he who first worked out the 
wonderful idea of parallax and applied it to the measure of 
distance. The highly ingenious theorem, determining the 
distance of the sun from the diameter of the earth's shadow, 
generally attributed to him, has already been noted. 

It was Hipparchus, probably, of all the ancients, who 
determined most accurately the distance of the moon, and it 
was he furthermore who understood the variations in its 
distance, who first drew a map of its path in space. His ideas 
on the grandeur of the sun were the same as those of Aristarchus ; 
and after all it made very little difference in the problem that 
was before them whether the diameter of the sun was six or 
eight times that of the earth or a hundred and six or eight 
times. The physical difficulty of conceiving the revolution of 
a larger body around the smaller was merely intensified by our 
modern methods, it was in no material way changed. More- 
over, Hipparchus must, have known of the ideas of Eratosthenes, 
who made the diameter twenty-seven times and the distance 
1 Simplicius, Scholia. 



THE FIRST IDEAS OF GRAVITATION 125 

a hundred times that of the moon ; he must have known it, 
because an extensive commentary upon Eratosthenes was one 
of his principal works. 

But the same hmitations which forced Hipparchus to the 
rejection of the heHocentric doctrines of Aristarchus, the same 
indifference to the mechanics of the problem, the disregard of 
considerations of relative weight and relative mass, would, it 
is obvious, have guided his mind away from, rather than toward, 
the problem of gravitation, the curious acceleration of the fall 
of bodies, and its possible connection with the circular move- 
ment of the planets. It is not so clear how this possible con- 
nection could have escaped the Titan mind of Archimedes. 

It is to the great geometer of Syracuse that we attribute the 
foundation of mechanics. The principle of the lever doubtless 
had been known for thousands of years, perhaps tens ; but 
it seems to have been Archimedes who worked out its theory 
and made it the basis of a science. Concerned with the problem 
of weight, the means of its determination, it was he perhaps of 
all the ancients who must have come nearest to the distinc- 
tion between weight and mass. He was profoundly interested 
in considerations of gravitation. Not merely the method of 
determination, but the idea of centres of gravity seems to have 
been his. It was Archimedes, as we have seen, who gave the 
explanation of why it is that upon a round earth the waters 
of the ocean did not run down the sides and spill away. 

Strangely did he not see the implication. Since bodies 
appear to be attracted towards the centre of a sphere, it follows 
that at the centre of the sphere this attraction will be zero. 
If it increases outward from the centre to the surface, what 
reason is there to suppose that it stops at the surface ? Not 
to the utmost height to which any of the huge engines Archi- 
medes constructed might hurl a heavy body was there the 
slightest evidence of the diminution of this force. The fall 
of meteorites, evidently from great heights, and pretty obviously 
under this same force of gravitation, carried the mind yet further 
outwards into space. It seems incredible that such a mind, 
working amid such problems and in contact with other minds 
like those of Aristarchus and Eratosthenes, busy with the 
measures of the moon and the sun, could not have made the 
one further step. 

Yet, as we shall see, the same limitations hemmed that 



126 THE WORLD MACHINE 

modern mind which most resembled the Syracusan's. Archi- 
medes did not make the measures of acceleration ; Galileo did, 
but as little to Galileo as to Archimedes did the light come. 

It is to be noted, apropos of the failure of Archimedes, that 
they seemed to lack in that day a minute and accurate measure 
of time. They had hour-glasses, and the clepsydra, a water- 
clock. They understood well how to " weigh " time — that is, 
to measure in the balance the amount of water or mercury 
escaping in the interval covering any given action to be observed ; 
but while it has been used with more success in our modern 
day, it was a clumsy method. It is evident that it was Galileo's 
discovery of the pendulum and his application of it as a pulse- 
counter, which opened the way for his measure of the rate 
of acceleration — yet another among ten thousand instances of 
the dependence of progress and discovery upon machines, that 
is to say, mechanical devices supplementing the crude human 
implements of hands and eyes. 

It is curious to reflect what might have been the effect had 
the measure of acceleration been made. They had a highly 
developed geometry, an astronomy as well. They knew the 
distance of the moon, and its size, almost as well as Newton ; 
they knew its orbit, and could calculate the distance it falls 
toward the earth, each moment of its flight, almost as well 
as he. Galileo's Discourses and Mathematical Demonstrations 
concerning Two New Sciences, dictated by a blind old man 
under confinement at the hands of the Roman Inquisition, 
appeared in 1638 ; therein these measures were first related. 
Newton's *' Mathematical Principles of Natural Philosophy," 
the Principia, in which the law of gravitation was announced, 
was given to the world in 1687. Just half a century lay 
between. 

When Xerxes crossed the Hellespont, says Diogenes, Anaxa- 
goras was twenty ; he was born, then, about the year 500 B.C. 
The sack of Syracuse and the butchery of Archimedes came 
nearly three centuries after. Three centuries later still the 
University of Alexandria and its great line of physical investi- 
gators still flourished ; Ptolemy, the astronomer, was writing 
his Syntaxis — the Almagest, and his treatise on the refraction 
of light. 

Six hundred years ! Time moved slowly then. Though in 
the reign of Neku I., 600 B.C., Phoenician mariners might achieve 



THE FIRST IDEAS OF GRAVITATION 127 

the circumnavigation of Africa ; though before the Christian 
era the rotundity of the earth was taught to children throughout 
the Greek world, and though Strabo had conjectured the exist- 
ence of " many other habitable places " far beyond the Pillars 
of Hercules, there was no Greek or Phoenician Columbus to 
venture across these uncharted wastes — they had no " guiding 
arrow." So, in the same way, there was no great organising 
brain to put together the geometrical demonstrations of Aris- 
tarchus, the mechanical constructions of Archimedes, and the 
conjectures of Anaxagoras, and thus, as it were, disclose the 
mechanism of the world. They had no reliable measure of 
seconds, and they lacked a science of dynamics — a mechanics 
of moving bodies. 

The foundations had been admirably laid by Archimedes ; 
but he seemed to find no followers to carry on his work. The 
sword which estopped that marvellous brain seemed to strike 
down not a man but a school ; he had practically no successors. 
In pure astronomy Hipparchus and Ptolemy made brilliant 
discoveries ; but there was no further advance toward a 
mecanique celeste. Though Ctesibius, at Alexandria, could 
invent suction-pumps and fire-engines ; though his more famous 
pupil, Hero or Heron, could invent the steam-engine and other 
marvels, they were of no use, they bore no fruit. 

There was a something in the spirit of the age which was 
fatal to any advance. The organisation of society into masters 
and slaves brought just such a contempt of industry as was 
to be seen in England in the land-owning days, and in the 
southern States before the war. The whole atmosphere of the 
time was simply stifling to practical things. Industry, labour, 
was the vile occupation of slaves ; mechanics, as we see in 
Plato, was an art despised. Experimental science, almost 
wholly dependent on mechanical devices, could not flourish. 

Perhaps, too, it would be hopeless to suppose that men 
would look for, or readily accept, mechanical explanations of 
phenomena until they had grown accustomed, in their daily 
lives, to the workings of machinery, and the obvious relations 
of force and matter, of energy and work. 

After Hero, in a thousand years, you cannot find trace in 
all Christendom of a new instrument or a new tool. After 
Ptolemy and Galen the spirit of initiative, of investigation, 
seemed to disappear. Exhausted by incessant and savage 



128 THE WORLD MACHINE 

warfare, debauched by universal slavery and superstition, their 
brilliant and slender civilisation went down. The advance of 
six wonderful centuries came to an end. What had been learned 
was forgotten. For the space of ten centuries after there is 
not an experiment, not an inquiry, not a book, not a tract, pro- 
duced in Europe that is worth ten lines in a history of human 
thought. The empire of the mind was given over to Platonising 
mystics and to dreary theologasters. 

On the side of astronomical investigation, then, Greek science 
just failed by a step to attain the point upon which our modern 
world conceptions are pivoted : the representation of cosmos, 
and more especially of the planetary system to which we belong, 
as a mechanism. — Was there any other path by which the 
human mind might reach the same point of view ? 

In that English Lake Country, where the charm of the land- 
scape grows by times so intimate and penetrating as to stir 
the heart of poet and dizzard alike, there lived at the beginning 
of the last century a Quaker schoolmaster, a diffident and retiring 
man, who filled his vacant hours studying the weather and the 
rain-gauge. They say that this John Dalton got to wondering 
about the process of evaporation and how it could be effected. 
It was a small beginning ; to it our modern atomic theory and 
the foundations of modern chemistry are due. Though he did 
not seem to know or care, Dalton had a forerunner among the 
same old Greeks, who, from much the same beginnings, followed 
nearly the same course of thought. 

If we look back into that ancient day, we shaU meet with 
a solitary and dominating figure, attached to no school, pursuing 
his own way, a profound and original investigator, perhaps 
as near to a universal genius as this world has ever known. 
Who was this Democritus of Abdera, the whole of whose two 
and seventy works Plato wished to burn, and of which time, 
not more lenient, has left us scarce a page ? 



CHAPTER XI 

DEMOCRITUS AND THE CONCEPT OF AN 
ATOMIC UNIVERSE 



And therefore the natural philosophies of Democritus and others 
who allow no God or mind in the frame of things, but attribute the 
structure of the universe to infinite essays and trials of nature, or 
what they call fate or fortune, and assigned the causes of particular 
things to the necessity of matter without any intermixture of final 
causes, seem, so far as we can judge from the remains of their 
philosophy, much more solid, and to have gone deeper into nature, 
with regard to physical causes, than the philosophy of Aristotle or 
Plato ; and this only because they never meddled with final causes, 
which the others were perpetually inculcating. 

Bacon, Advancement of Learning. 



CHAPTER XI 

DEMOCRITUS AND THE CONCEPT OF AN 
ATOMIC UNIVERSE 

It was late in the intellectual awakening of Greece that Athens 
became its centre. While the little peninsula, whose after 
life was to shed such a glow in the world, was given over to 
the sack and slaughter of warring tribes, the shores and the 
islands of the ^Egean were astir with a varied activity. There, 
and along the coasts of southernmost Italy, the Doric and Ionic 
Greeks, driven from the mother-land, had flung wide their line 
of colonies. They were navigators and merchants, pirates, 
too, perhaps ; they vied with the Phoenicians for the trade 
of Egypt, and whithersoever they went, they planted their 
depots and grew rich. And with nations as with the nouveaux 
riches always, with their wealth they became civilised, built 
palaces, and dabbled in philosophy and art. Some of their 
people, the Sybarites, in Italy, studied so well the ulterior re- 
finements of pleasure as to supply luxury with a synonym. 
In Miletus on the Asian shore, Thales, and with him Greek 
physical inquiry, was born. For a century or so half the great 
names in Hellas were Ionian. 

At the top of the iEgean where it washes the coast of the 
ancient Thrak6, now a part of the Turkish dominion, lay the 
Ionian city of Abdera. In that time it seems to have been 
noted for its prosperity and general culture. It must have 
been very rich, for there is a legend that when Xerxes came 
with his Persian hordes on their way to Thermopylae, he was 
entertained in Abdera by a private citizen. As a token of 
time well spent, Xerxes, so the legend runs, left with this 
Hegisistratus certain magi or wise men, for the instruction of 
the rich man's sons. One of them, Democritus, must have 
been a marvellous pupil. When he had learned all the magi 
had to impart, he took his share of the parental estate in coin 
of the realm, and diligently squandered it in seeing every corner 



132 THE WORLD MACHINE 

of the earth he could reach. True, the accessible world was 
not then very wide ; be that as it may, the youth returned 
when youth was gone, versed in all the priestly lore of Egypt 
and Chaldea — rich beyond any contemporary in knowledge, 
and without a sou. 

There in his native Abdera he thought and worked, observed 
incessantly, tested minutely his perceptions and his sensations ; 
joked too, it seems, reflected, read, and wrote. By-and-by, in 
the public square, Democritus opened the pages of his great 
work, Diakosmos, and read aloud to him who would listen. It 
was said that he predicted the weather, and other events as 
well, and remembering his training at the hands of the magicians, 
the simple Abderites had little trouble in believing him very 
near a god. Pliny tells a story of how he could raise the dead ; 
but this, of course, was a common legend of credulous antiquity, 
and told of many men. 

Whether he did or no, they put up votive tablets in his 
honour whilst yet he lived, and as there was then a law that 
whoso had spent his patrimony should be denied a decent burial, 
'tis told they gave the philosopher a purse of five hundred 
talents. The sum is large; the revenues of Alexander's 
empire were annually scarce so great. The historians of that 
day were as prodigal of money and numbers as the Chinese 
of time. No matter, 'twas said he laughed so hard at all the 
follies of the world, some thought him mad, and sent for the 
famed Hippocrates to cure his distemper. But Hippocrates, 
when he had come, smiled and went away, remarking upon 
the charm and fascination of his discourse. 

He lived to be fabulously old — a hundred or more ; but 
before he had finished he seems to have swept through every 
science known to his day. Diogenes Laertius gives a list of 
seventy-two of his books ; not one remains. We may regret 
the loss, for not only does he seem to have had one of the most 
acute and piercing minds of any age, but evidently he knew 
as well the witchery of the syllables, the charm of the cadenced 
period, the enchantment of the deftly-woven phrase. It is 
the testimony of Cicero, and here at least there could be no 
weightier judge, that he wrote in a style which, for its poetic 
beauty, was worthy to set beside that of Plato. 

He was a modest man ; he began his chief work, " I am 
going to write of everything," and he very nearly did. If we 



CONCEPT OF AN ATOMIC UNIVERSE 133 

may judge from a fragment, he prided himself most on his 
travels and his skill in geometry, for he says : — 

" Of all my contemporaries, it is I who have traversed the 
greatest part of the earth, visited the most distant regions, 
studied climates the most diverse, countries the most varied, 
and listened to the most thinkers ; there is no one who has 
surpassed me in geometrical constructions and demonstrations, 
no, not even the geometers of Egypt, among whom I passed 
five full years of my life." ^ 

The mere list of his studies reveals their extraordinary 
range. Aristotle, we know, left a work on some of Democritus' 
theorems, and there were few philosophers in antiquity who 
did not write for or against him in some way. He seems to 
have been abreast, if not in advance of the astronomy of his 
day ; he writes on the Planets, the Map of the Heavens, the 
Great Year, and much else. He was a geographer, and wrote 
a treatise on that and on Navigation by means of the Pole- 
star. He was learned in physics. We read with especial interest 
of a work on the Magnet, others on Rays of Light, on the 
Clepsydra, or water-clock. He was evidently fond of music 
and poetry, for he left treatises on Rhythm and Harmony, on 
Song, on the beauty of the epic poems, on Homer. He counted 
himself a critic in matters of art, evidently, for he wrote on 
Painting. He must have been a physician, for he left a book 
on Fever, another on Dietetics, or The Opinions of a Physician ; 
another on Prognostics, another on Pestilences, another on the 
Right Way of Living. We find another on Agriculture, and 
Causes Affecting Seeds, a book on Tactics, and Fighting in 
Heavy Armour, possibly not his, a discourse on History, a book 
on the Principles of Laws, a discussion of the Calendar, another 
on Colours. He writes on Pythagoras, whom he seemed greatly 
to admire ; he gives us a sketch of the Disposition of the Wise 
Man, an essay on Cheerfulness, a number of others on Ethics 
and similar topics. 

He was a zoologist and an anatomist ; 'twas said he practised 
dissection, and we find a work on Animals. He was a psycho- 
logist, and we find an essay on the Mind, another on the Senses. 
We have a glimpse of his penetration and his knowledge in his 
ideas as to the seat of the mind. Aristotle had no conception 
of the truth ; he fixes it in the heart. A hundred years before 
1 MuUach, Frag. Philos. Gvcbc, 370. 



134 THE WORLD MACHINE 

Democritus had found in the brain " the monarch of the 
body." 

These were his works ; and you gather that his was one of 
those omnivorous minds which range everywhere, consume all 
things. You surmise that it may have been also one of those 
ragbag minds which in the end produces a crazy quilt like the 
Anatomy of Melancholy, No, he is a thinker, an intense and 
originating genius, ein bahnbrecher, as the Germans have it. 

When we consider the fragments of his philosophy as they 
have been preserved to us by his critics, his detractors and his 
friends, it seems as if there were few things betwixt heaven and 
earth that he had not thought upon. He preceded Descartes 
by two thousand years in the consecration of doubt. He was 
a sceptic twenty centuries before Hume. He explained, " we 
know nothing really, for the truth lies in the depths." 

Democritus endeavoured to reduce all sensation to the 
primal sense of touch, as we learn from Aristotle, who blames 
him. In this he precedes many a modern thinker. So far as 
we know he was the founder of the sensational school ; at least 
he wholly anticipated Locke. He clearly discriminated between 
" primary " and " secondary " qualities. ** What is cold is cold 
in opinion, and what is hot is hot in opinion." He saw that 
there is a class of sensations that is wholly subjective and that 
exists only in the mind. 

His seems to have been a fertilising mind, a kind of a fount 
from which others draw their store copiously and without stint 
— after the fashion of the ancients, too, largely without 
acknowledgment. 

Eucken says that Aristotle copies from him page after page, 
and gives little credit ; MuUach conjectures that the Stag5n:ite 
was in great part indebted to the Abderan for the reputation 
of vast learning he gained. Cicero tells us that Epicurus 
borrowed bodily all of his physical theories, his philosophy as 
well ; spoils what he borrows and gives no credit at all. It is 
evident that Democritus acquired a great renown, else why 
should Aristoxenus say that Plato wished to burn all of his works 
he could lay hands on, " but was prevented from so doing." 
Cicero, again, of a whoUy opposing school of ideas, yet says : 
" Who is there whom we can compare with him for the great- 
ness, not merely of his genius, but of his spirit ? "—What were 
his ideas of this world ? 



CONCEPT OF AN ATOMIC UNIVERSE 135 

Remember that he came four hundred years before Cicero, 
a full hundred before Aristotle, a century and a half before the 
founding of Alexandria. He was the contemporary of Pericles, 
of Phidias, and of that Socrates who said of astronomy that it 
was " impossible to understand and madness to investigate." 
Apparently he did not have the idea of a rotund earth, a fact 
that is the more astonishing in the face of all his other cosmical 
views, and because he was the friend of that Philolaus of 
Crotona, who may have been the first in Greece to proclaim 
the motion of our globe. 

Not over laden, then, is the glowing phrase wherein M. 
Martha remarks of the ideas of " this great philosophical 
geometer, who by the sole intuition of a penetrating genius, 
and without the resource of those instruments which chance 
has subsequently given to modern science, had penetrated many 
mysteries of the heavens." He appears clearly to have antici- 
pated Aristarchus ; he taught, for example, " that the sun is 
not the small disk such as we see, but is of immense size ; that 
the Milky Way is an assemblage of stars, which from their 
distance elude our sight, and which by reason of being so thickly 
sown in space, illuminate each other ; and that the shapes one 
sees in the moon are to be attributed to the heights of its 
mountains and the depths of its valleys." ^ He held, moreover, 
to the idea of the infinity of worlds, their slow but incessant 
destruction and reformation ; for him as for us the stars were 
suns. Amazing previsions, that the advance of knowledge has 
so strikingly confirmed ! 

Here was enough, no doubt, to lift Democritus far out of the 
tribe of quibbling pedants who passed for philosophers in those 
opulent days. He was no mere shriftsteller ; no superficial 
Aristotle, no shallow, empty and pretentious Bacon. We have 
now to see how, by the sheer force of his reasoning, he could 
rise to a world conception which, in its main features, is still 
the most tenable we possess. 

Democritus, like John Dalton, was evidently a weather 
sharp ; it was the success of his predictions in meteorology 
which gained him so great a vogue among the Abderites. We 
may picture him watching, like Dalton, the water in a stone 
crock disappear in the sunshine, wondering how it could be 
taken up into the air, as so it must have been. He had heard, 
^ Martha, Le Poeme de Lucrice, 239. 



136 THE WORLD MACHINE 

no doubt, of the notions of Anaxagoras, that all things are made 
up of homeomericB, or similar parts ; of the ideas of Leukippus 
as well. It seems to have been the latter who first pictured 
bodies as made of indivisible particles or atoms. The spirit 
of inquiry was in the air, and Democritus, starting from these 
suggestive ideas as did Spencer from the speculations of von 
Baer, was carried far. The scheme of the world, as it shaped 
itself in the mind of Democritus, was crystalline in its simplicity. 
The ring upon the finger, the stone steps before the door, the 
toe of the graven saints under the incessant kisses of the faithful, 
wear away, subtly, imperceptibly, without that from day to 
day one may perceive aught of change. The pot, boiling upon 
the hearth, the pools of water in the sun, dry up ; their con- 
tents disappear, one scarce knows how. Linen, hanging by the 
shore, before a beating surf, becomes damp ; expose it to the 
heat, it dries again. Evidently the water, the stone image, 
the metal of the ring, is made up of particles too fine to be 
visible or perceptible to touch. 

Doubtless the same is true of all matter whatsoever, whether 
it be " living " or " dead." The grain sprouts, the stalk forms, 
the flowers or the great oak unfurl, in precisely the same way 
as the idol's toe disappears, subtly, imperceptibly, elusively. 
Obviously they are formed by the aggregation, as the others are 
destroyed by the disaggregation, of exceedingly minute parts. 
We witness the same process when a lump of sugar dissolves 
in a glass of water, or when a layer of salt crystallises out of a 
pan of salt water when it is evaporated. 

When the sugar or the salt disappear in the solvent, how 
far does the process of disaggregation go ? — infinitely ? We 
may take a glass of salt water and mix it with another of fresh ; 
the salt taste grows a little weaker ; but it is evenly distributed 
throughout every drop of water. Repeat the process, and the 
result, though the salt taste grows still fainter, is the same. 
May we keep on doing this for ever ? By-and-by the salt taste 
is gone utterly ; but we have only to evaporate the mass of 
water again and secure all of the salt ; none has disappeared. 

But how far can the process of disaggregation be carried ; 
how finely can the grains of salt be split up ? So constituted 
is the human mind that any limit is unimaginable. We cannot 
think of an object so small that it cannot be cut in two, each 
of these parts divided again, and again, and again, and so on 



CONCEPT OF AN ATOMIC UNIVERSE 137 

world without end. We may pursue the operation to the 
mental extinction of infinitude, and the mind will set no bar. 

But, on the other hand, it is equally unimaginable that any 
number of parts or particles, infinitely smaU, can make up an 
actual tangible something, when brought together. We may, if 
we like, try to conceive of an infinitude of infinitesimals ; but a 
collocation of these for every grain of salt or sugar is a trifle 
wearisome, to say nothing of the fact that it eludes clear mental 
presentation. Common-sense folk will hardly waste good time 
over such cobwebs, though it is curious to recall that this seemed 
the most satisfactory view to such an eminently practical and 
concrete mind as Faraday's. 

For the ordinary affairs of life, our bodies, so alive to pain, 
the foods we eat, so needful, the liquids we drink, the gases 
without which we cannot for a moment survive, the houses 
we live in, the stones we tumble over, seem very real. So do 
the folk, disagreeable and agreeable, that we find about us ; 
the earth we tread, the hills we climb. How account for their 
existence ? Democritus chose the least tenuous of the two 
unthinkables : the infinitely divisible and the finitely indivisible 
— that is, the latter. He called these ultimate particles by a 
name which described them just as he thought of them, as 
a-tomic or undivisible — that is, atoms. 

Doubtless in this he had many predecessors. Some such 
idea must have drifted across the mind of many a thinker many 
hundreds of years before. It is a conception that must soon 
unfold in any reflecting mind. If a chink in a wall lets through 
a beam of sunlight into a darkened room, seen sidewise the 
air is full of dancing particles. It is merely an illusion of the 
senses, then, to think of the room as empty. It is full of 
dancing motes. If we are very careful to leave a room un- 
disturbed, by-and-by on objects in the room a fine dust gathers, 
and the motes wiU have almost disappeared from the sun's 
gleam. 

Evidently, then, these motes are not air ; but float in the 
air. And if they can float in the air, even as other bodies float 
in water, then the air is equally real, conceivably also made up 
of parts or atoms. It is perfectly clear that so Democritus 
thought of it. In the pages of Lucretius, in which the thoughts 
of Democritus, filtered through the writings of Epicurus, re- 
appear after three or four centuries, there is a vivid and striking 



138 THE WORLD MACHINE 

argument to prove that the air is material, that it has weight ; 
they had, in brief, very much the same idea about it as we have 
now. They probably had no air-pump to make a vacuum ; 
but they could observe the tremendous force of the winds when 
this same air was set in motion. From the gentlest zephyr 
to the wild tornado which could throw down the walls of houses, 
uproot trees, even cut them off sharply as if they had been 
smitten with an axe, there was no gap. One graded into 
another. It was very clear that the air, in its way, is just as 
real a substance as water, even though in so many ways it 
escapes our senses. 

Over the illusions of sense, indeed, Democritus seems to 
have spent a deal of time. It is told of him that he used to go 
out into his garden, where he could be quite unobserved, and 
spend hours upon hours " testing his senses." It is fine mental 
exercise. Nothing can open the gateways of the mind more 
surely to the great thoughts that came to his. 

Perhaps it was from the suggestion of the motes in the sun- 
beam that Democritus rose to the conception of particles not 
merely indivisible but invisible as well, and far beyond the 
palpation of the senses. It is only in their aggregations that 
they became sensible, yet of them aU things are made. Their 
aggregations may be as minute as the particles of air, the motes 
of the beam ; they may be worlds and suns. For Democritus 
space was infinite ; through space the atoms rained downwards 
for ever in an infinite stream ; they fall by reason of their 
weight, the heavier particles falling faster than the small ones. 
This gives rise to clusters or clumps of atoms, these in turn to 
others, until you have the solid stuffs which our hands may 
grasp, our eyes may see. 

Democritus pictured these atoms as indestructible as well. 
Two thousand years before Lavoisier he clearly saw that the 
forms of matter change, but none is lost. In the transmutation 
of the atoms we have the varied shapes of things ; but as to 
the elements of matter itself, there is no annihilation, no 
creation. Nothing comes from nothing. That was a dogma, 
doubtless, that was very old before Democritus came upon the 
scene, but no one that we know of in that ancient day taught 
it so clearly, or,iollowed it so far. 

He had, then, the first of the two great " laws " which our 
modern time regards as fundamental to aU experimental science. 



CONCEPT OF AN ATOMIC UNIVERSE 139 

So far as mere philosophical reasoning could carry him, he had 
the second as well. Ideas of force and energy were nebulous 
enough in those days. Forces could hardly be studied before 
they were known. Of electricity the ancients knew practically 
nothing at all ; of magnetism, but little more. They had 
observed, of course, that some substances, like amber, repelled 
or attracted light particles when they were smartly rubbed up 
with flannel or cat's fur ; but the idea of associating this with 
lightning of the thunderstorms on the one hand, with light 
and heat on the other, probably never entered their minds. 
Nor could they have had any very clear idea of the relations 
of electricity and the actions of the magnet. 

Nor, again, could very definite ideas of energy arise before 
they had developed the science of dynamics and begun to invent 
and to use varied machines. It was beyond the powers of 
any man, therefore, then to conceive the doctrine of the con- 
servation of energy — at least in its modern sense — that is, the 
idea that there is no motion, no force, no power to do work which 
is ever ** lost " to the universe ; that energy, as little as matter, 
cannot be created nor destroyed. Yet the idea in all its 
essentials Democritus had unequivocally attained. He had 
reached even the distinction between force {Svvafus) and energy 
{hepyetn) which we regard as a fruit of our own time. 

His ideas waited many centuries for definitive experimental 
proof ; but that in no wise detracts from the merit of his 
genius. He was the father of modern physics and of modern 
chemistry as well. True, the idea of chemical affinity, of 
attractions among the atoms, did not come into his system ; 
that was reserved for a later day. But, Empedocles* vague 
poetical concept of loves and hates among the atoms disre- 
garded, there was no one, apparently, among the ancients who 
got any further than he. When in our modern time men again 
began to turn their minds to physical problems, it was to begin 
where Democritus left off. 

The Abderan philosopher founded no school. His philo- 
sophy and his system were far too severe for the volatile and 
phrase-loving Greek mind. So we find here, as in the field of 
astronomy, that a space of eighteen or twenty centuries inter- 
venes before any further progress is made — before, indeed, there 
was apparently any further thought upon the subject at all. 

In the sixteenth and seventeenth centuries we find philo- 



140 THE WORLD MACHINE 

sophers going over the same ground and digging from obscurity 
Democritus' ideas. Along about the middle of the seventeenth 
century we find Boyle utilising them to found the modern science 
of chemistry. A little later, with Newton, was revealed the 
law of that force of attraction which exists between every 
atom of matter in the universe. 

Democritus has often been styled the'grandsire of materialism. 
It is a school of philosophy that is a little out of fashion nowa- 
days ; yet it is worthy of note that practically all of the modern 
advance in our ideas of this world has been grounded upon 
his conceptions. Practically speaking, materialistic assumptions 
are simply unescapable in physical investigations. But it is 
to be noted that philosophically Democritus was far from the 
crude dogmas of Buchner and his kind. It is difficult to judge 
of a doctrine from fragments. Moreover, as dreary shelvesfull 
of vacuous volumes on the history of philosophy so amply 
attest, it is possible to read into the ideas of the ancients much 
of anything that one likes. But so far as one may judge, 
Democritus in his order of ideas came nearer to those of 
Herbert Spencer than perhaps any of our moderns, with the 
difference, perhaps, that to the Underlying Reality he gave a 
name where Mr. Spencer declined. Both recognised equally 
that the ultimate is in its essence unknowable ; " the truth lies 
in the depths." 

If Democritus is to be accounted a materialist at all, it 
must be in that larger Tyndallian sense which sees in matter 
" the promise and potency of all terrestrial life." This was 
clearly the teachings of the Abderan. The body was made up 
of material atoms, the brain as weU ; the mind is a function of 
the brain, and for him the soul was the mind. It was made up 
of " fine smooth round atoms, similar to the atoms of fire " ; 
these are the most mobile of all ; penetrating the body, they 
give rise to the phenomena of life. Substitute for the " fine 
smooth round atoms " of Democritus the " animal spirits " of 
Descartes — and we know as much of one as the other — and it 
wiU be perceived that his ideas did not differ very differently 
from those of the founder of modern neurology. 

Thing curious to note : so far as modern thought forms 
any picture of mind, memory, and the soul, it is largely along 
lines of Hartley's vibrations, to all intents a parallel to the un- 



CONCEPT OF AN ATOMIC UNIVERSE 141 

dulatory or vibratory theories of energy. Conceive our ether 
theories of light and electricity falling to the ground and 
Newtonian conceptions of corpuscles coming back in their stead 
— we should needfully revert to essentially Democritan ideas 
for our picture of mental processes. 

Be this as it may, and whether we choose to regard this 
early prophet of the Unknowable as a materialist, what is cer- 
tain is that we owe to Democritus, so far as our knowledge 
extends, the idea of a world machine. His mechanical con- 
ceptions, the mechanical conceptions of the ancients, could 
scarcely have been the replica of ours. Such steam engines 
as existed seem to have been little more than toys, or machina- 
tions of the priests to strike terror and wonder into the minds 
of the vulgar. Nor is it in the least clear that Democritus 
had a mechanical turn of mind like, for example, Archimedes, 
Archytas, or Hero of Alexandria. But in his idea of all existing 
things as made up of particles, these particles in their motions 
able to do work, to exhibit energy, Democritus had, in its 
essence, a purely mechanical conception of the phenomenal 
world. His atoms were its instruments. 

Atoms and space, matter and the motions of matter, and 
nothing more ; you perceive the consequence. If motes and 
moons, if worlds and waters, if insects and trees, and all things 
else but represent the permutation of eternal atoms, what we 
call chance is but a phrase with which we clothe our ignorance 
of events. From the simple combination of the atoms result 
the phenomena which we observe, the events of which we are a 
fleeting part. 

Democritus does not seem to have proclaimed himself an 
atheist any more, for example, than did Mr. Spencer. Among 
the Greeks the first of the deniers of the gods and their rule 
of this world seems to have been his disciple Protagoras. We 
gather that Democritus may have conceived the existence of 
a race of super-men ; but if they existed, even these were a 
part of a scheme which persisted through space and time. In 
the Democritan concept, if there was a god, its name was law. 

It is needless to add that Democritus admitted no such 
thing as freedom of the will. Since all was enchained ; since 
one event inevitably follows from another ; since, again, in the 
order of things which exists nothing can ever happen otherwise 
than as it does, Democritus pictured all phenomena, the actions 



142 THE WORLD MACHINE 

of our human kind as well, as governed by a rigid and unescap- 
able necessity. 

There are types of mind which recoil from this conception of 
the world with a kind of fright. For Democritus it seemed to 
have no such terror. He taught that the highest good was 
tranquillity of mind ; he preached cheerfulness as the most 
admirable of human qualities, and what is more to the point, 
he seems to have practised it as well. He appeared thoroughly 
to enjoy life, for all his ideas ; it may be because of them. At 
any rate, he lived to a green old age, and by a curious fate 
passed into the history of Greek thought as " the Laughing 
Philosopher." 

There might be profit in his example for our modern men 
of science, who seem to take their learning a trifle seriously 
and with little relief of gaiety. One would imagine they most 
times forget that science, like letters or art, can have hardly 
any other aim than to make life a little easier, a little pleasanter, 
more varied, more interesting, more serene. Democritus, we 
may believe, did not. 



CHAPTER XII 

THE LEGACY OF THE GREEKS: THE 
REBIRTH OF TIME 



What we are is in part only of our making ; the greater part of 
ourselves has come down to us from the past. What we know and 
what we think is not a new fountain gushing fresh from the barren 
rock of the unknown at the stroke of the rod of our own intellect ; 
it is a stream which flows by us and through us, fed by the far-off 
rivulets of long ago. As what we think and say to-day will mingle 
with and shape the thoughts of men in the years to come, so in the 
opinions and views which we are proud to hold to-day we may, by 
looking back, trace the influence of the thoughts of those who have 
gone before. Tracking out how new thoughts are linked to old ones, 
seeing how an error cast into the stream of knowledge leaves a 
streak lasting through many changes of the ways of man, noting 
the struggles through which a truth now rising to the surface, now 
seemingly lost in the depths, eventually swims triumphant on the 
flood, we may perhaps the better learn to appraise our present 
knowledge, and the more rightly judge which of the thoughts 
of to-day is on the direct line of progress, carrying the truth of 
yesterday on to that of to-morrow, and which is a mere fragment 
of the hour, floating conspicuous on the surface now, but destined 
soon to sink, and later to be wholly forgot. 

Sir Michael Foster, Hist, of Physiology, 



CHAPTER XII 

THE LEGACY OF THE GREEKS: THE 
REBIRTH OF TIME 

The appraisal of the Greek achievement has varied widely. 
To the scholars of the Renaissance it seemed wondrous. In our 
later day it has suffered somewhat from neglect. " It may be 
doubted," says Huxley, '* if even-handed justice, as free from 
fulsome panegyric as from captious depreciation, has ever yet 
been dealt out to the sages of antiquity, who for eight centuries, 
from the time of Thales to that of Galen, toiled at the founda- 
tions of physical science." 

The observation is just ; the explanation perhaps is not 
distant. The quality of mind which finds adequate mental 
pabulum in the mere records of another people or another time 
is not high. It will as a rule be ignorant of the achievements 
of its own age. It will then reckon large the deeds of antiquity. 

On the other hand, the modern man of science, dipping 
into the ancient day, is impatient with what to him seem in- 
excusable absurdities. He is accustomed to exact methods of 
research, and the Greeks were not exact. Accuracy and pre- 
cision are to him the elementary principles of investigation, 
and the ancients often failed even of that degree of accuracy 
which was readily attainable from the instruments and methods 
they employed. The modern mind is trained to rigorous 
demands for proof ; the ancient mind was not. Plato and 
Aristotle are credulous to a degree which in the most ordinary 
man of enlightenment to-day would render him absurd. 

And again, the greatest measuring geniuses of antiquity, 
men like Eratosthenes and Poseidonius, seemed to have been 
quite content if the Hmits of error were within ten, twenty, or, 
in extreme cases, fifty per cent. It was not that they were 
uninstructed ; it was not that they lacked ingenuity. In the 
latter regard they have been surpassed by no modern mind. It 
was simply that the temper of the age was careless. So it is 

145 K 



146 THE WORLD MACHINE 

that the present-day hierophant, lacking somewhat the sense 
of historical perspective, draws a little the frowning brow as 
he contemplates the rather lighter-hearted science of that 
lighter-hearted time. 

Is it possible to effect a just adjudication ? Let us consider 
with Kant that the extent of knowledge in any given field is 
measured by the amount of mathematics which it contains, and 
make the attempt. We might think of the matter in this 
light :— 

The century that saw the end of the Roman Republic and 
the beginning of the Empire may be accounted the apogee of 
Roman culture. The glory of Alexandria was on the wane. 
There were richer prizes in the new world-capital. It was the 
time of Csesar and of Augustus, of Cicero and of Pompey, of 
Lucretius and of Virgil. It was an age of freedom and en- 
lightenment. The study of Greek philosophy and ideas was 
widespread. Greek physical investigation had practically 
reached its term ; its fruits had been gathered. They were 
then among the common possessions of mankind, and doubt- 
less taught to children as are the teachings of Newton and 
Darwin now. In what regard, let us ask, would a highly en- 
lightened Alexandrian, or his compeer at Rome, heritor of 
the Greek tradition and fully abreast of the knowledge of his 
time, differ, in his larger world ideas, from a man of the same 
temper and standing now ? 

It is evident enough from the pages of Lucretius, of Cicero, 
of Pliny, of Strabo, and of Cleomedes, that in many ways the 
difference was slight. The youth of that time were taught the 
geometry of Euclid. It is taught to the youth of our time with 
little addition and little change. The trigonometry of the 
Greeks was but slightly developed, their algebra scarce at all. 
Their system of notation was not decimal. It follows that 
they had no logarithms. The calculus was quite unknown. 
Their processes of computation were clumsy. There are some 
problems which the modern mind has solved by means of the 
higher mathematics. But in a large view it is doubtful if there 
was any fact of deep import which was beyond the powers of 
Greek methods of analysis. 

In their application of mathematics to the mensuration of 
space, time, and mass, alike their methods and their instru- 
ments were crude ; yet the accuracy attained in the construe- 



THE LEGACY OF THE GREEKS 147 

tion of the pyramids, several thousand years before this era, 
is sufficient evidence that for most practical concerns they 
were not greatly inferior to our own. 

Some of their methods were roundabout. They calculated, 
for example, the visual diameter of the sun from the time which 
elapsed between the appearance of its edge above the horizon 
to that in which its full disk was visible. They did this by 
weighing the quantity of water which ran from one vessel into 
another in the interval. Such means of observation seem to 
us primitive. It is to be noted that they were fairly effective. 

They had applied mathematics to the problems of mechanics, 
of optics, of acoustics. They understood the elements of musical 
theory — that a vibrating string divides successively into halves, 
thirds, and so on, and that the notes of the scale are in simple 
ratio to the fundamental tone. They understood the principle 
of the lever ; they had developed fairly well the statics of bodies. 
They had fairly well worked out the geometrical side of optical 
theory. They knew that the sun appears before it is actually 
above the horizon ; and from this Poseidonius was able to 
calculate with a fair approximation the height of the earth's 
atmosphere. Through the applications of geometrical optics, 
they were able to solve the more essential questions which 
pertain to the place of the earth in cosmos. Let us sum up 
precisely what they knew : — 

They understood that the earth is a sphere, and that it 
hangs, so far as any one may see, in empty space. Their minds 
had reached the conception that it rests on nothing. 

They understood the size of the earth, had fair ideas of its 
variety of climate, had measured accurately the width of the 
tropical zone. They knew in theory at least of the land of the 
midnight sun. They discussed with enlightenment the question 
of other habitable continents beyond the seas. They had fixed 
with close approximation the distance of the moon, and realised 
its great size. Some of them at least knew of the relations of 
the moon to the tides. 

They understood something of the distance and grandeur 
of the sun. They knew that it was a body far larger than the 
earth. Two of them at least had more correct ideas, had made 
better measures, than had any one before Cassini and Newton, 
fifty years after the telescope was in general use. The sombre 
reflections of Cicero and many another make it clear that the 



148 THE WORLD MACHINE 

moral of these astonishing measures had come home to them. 
Their minds, too, had left the inconsequence of earthly concerns 
in the face of cosmic immensity. 

They had correctly apprehended the character of the 
*' wandering " stars, and had set them in circular or epicycUc 
orbits, in revolution about the earth and the sun. They do 
not seem to have computed their relative distances ; but they 
had enough of an idea of the solar system to make mechanical 
models of it. 

They knew well the enormous distance of the stars, and they 
understood clearly that, compared with this distance, the great 
bulk of the earth was scarce more than a mathematical point. 
Some among them at least conceived the stars as suns. Sim- 
plicius, upon what grounds we do not know, stated that some 
of them were larger than our own. The infinity of worlds was 
a commonplace to which Lucretius and Cicero refer rather 
than contend for. 

Through five or six centuries — through a far longer time than 
our modern world has believed in the fact — a considerable sect 
among them, the Pythagoreans and their numerous adherents, 
taught the motion of the earth upon its axis. Some few among 
them taught as well the fixity of the sun and the movement of 
the earth about it. One among them at least had submitted 
the possible extent of the universe to a mathematical calculation. 

Their insight into the problems of more immediate terrestrial 
concern was less penetrating. The studies which we now group 
up under the name of the physical sciences found a much slighter 
development at their hands. They were metallurgists of long 
standing ; but of chemical theory they had next to none. Their 
ideas of heat and other natural forces were of the crudest. They 
had not deciphered the hieroglyphics of the rocks. Of true 
conceptions of the age of the earth, or its formation, or of world 
formation in general, they could have had none at all. 

And yet there were not wanting among them piercing minds 
which had caught some glimpse of our modern ideas. Zenoph- 
anes could find evidence of a time when the seas had stood 
above the tops of the highest mountains. Anaxagoras could 
look forward to a time when the highest mountains would be 
again beneath the sea. Empedocles caught distantly the idea 
of the immutation of the species. In Lucretius' marvellous 
poem " On Nature " there is a sketch of the struggle for exist- 



THE LEGACY OF THE GREEKS 149 

ence that is probably as good an account, on its larger side, 
of the Darwinian theory as, let us say, the late Matthew Arnold 
could have written without reference to some accepted exposition. 

In Pliny there are recipes for foretelling the weather. 
Democritus had written upon the same subject at a time more 
distant from Pliny than the later crusades from our own. 

It is evident enough that a very large number of minds 
had widened to the perception of nature as a series of pheno- 
mena, orderly and more or less predictable, and understand- 
able among themselves. It is evident that for five or six 
hundred years the clearer thinking portion of mankind had 
given over its beliefs in interfering deities and malevolent demons, 
and had quite ceased to look out upon creation with the naive 
fancies of their far forbears. 

Consider now the world ideas of some of the foremost men 
of letters, of politics, and of affairs in the present age. It is 
evident that there were among the ancients not single minds 
but scores who undoubtedly had better apprehended the scheme 
of this world than, let us say, Tolstoi or Mr. Gladstone, the 
last representative of the Russian autocracy, or the possessor 
of the greatest fortune in America. 

Again, let us ask ourselves, in what regard does the average 
man, even among the most enlightened, nowadays pursue the 
game of life in a manner different from the busy traders of 
Alexandria or the land-holders of the Roman Empire ? Then, 
as now, money ruled the world. Then, as now, the central 
power of the State was a plutocracy. Then, as now, politics 
was a road to wealth. Caesar left Rome for Spain at thirty- 
eight or so, owing 250 million sesterces — perhaps two million 
sterling. He died worth perhaps as many more. Crassus 
became the wealthiest man in Rome through real-estate specu- 
lation, just as did George Washington, and by building houses 
to sell, doubtless on the instalment plan. Then, as now, to be 
rich, to marry among the rich, to have a place among the society 
of the rich, to win applause or secure political preferment by 
scattering a fortune with a lavish hand, was the supreme desire 
of the great body of mankind. 

' Scientific investigation then interested but few. It interests 
but few now. The number of men of culture and intellectual 
distinction, of freedom from the prejudices and passions of the 
vulgar, from the cant of religion or patriotism or a smug and 



I50 THE WORLD MACHINE 

unctuous morality, of high aims, of a large and wide-eyed 
humanity, was scant then as it is scant now. They were the 
remnant set over against the vast majority, as they are the 
remnant set over the vast majority still. 

Three or four centuries of Hellenic freedom from superstition, 
of clear thinking and a rational investigation of nature, could 
not transform the mind of the populace, just as three or four 
centuries of modern scientific development has not transformed 
it. If the spirit of rationalism in its modern day renascence 
has struck deeper, has taken a firmer hold, the fact is due to 
forces in some sense extraneous to the scientific spirit. It is 
because of what we have come to call applied science, the 
practical use of knowledge, the development of machinery, 
and the consequent diffusion of comfort and advantages, that 
our own time is cleaner, saner, less cruel, less brutal, less credulous, 
than that of two thousand years ago. 

To sum up : Hellenism, Hellenic art, literature, science, 
was a stage — all things considered, a very high stage — far 
nearer to our own than anything in the twelve or fifteen centuries 
which intervened. It was by a slender space that the Greek 
mind failed wholly to anticipate our present-day cosmical theory. 
They had attained to grandiose ideas of infinitude, which 
modern research has somewhat extended but not changed. They 
had gained, in all its fundamental characters, a true representa- 
tion of the place of this earth in space, its form, its size, its 
motion, the grandeur of the sun, the distance of the stars — 
in brief, a correct and reasoned picture of creation as it is. 
There were giants among them who would be giants no less, 
and, it may be added, no more, to-day. They reasoned as we 
reason, measured as we measure ; their achievement was im- 
mense ; it deserved to endure. 

What we may regard as the crowning discovery, they missed. 
The conception of a single mechanical force acting across the 
furthest confines of the universe alone was wanting. This idea, 
which was finally to banish the crude notions of the inter- 
vention of gods and demons in the course of the heavens, which 
eventually was to destroy the notion of the intervention of 
gods and demons in the affairs of men, finally and for ever to 
estabUsh the idea of a universal order and universal law, they 
lacked. Let us not on this accoimt belittle the splendour of 
their deeds. 



THE LEGACY OF THE GREEKS 151 

It is with a melancholy interest that we reflect that this 
exquisite flowering of the human intellect was to pass utterly 
away and to be forgotten for a thousand years ; that a craven 
and baseless superstition was to come in the stead of this 
civilisation of beauty and of light ; that the empire of life 
and mind was to be given over to venal and licentious monsters 
robed as the vicars of the Most High ; that the race should be 
despoiled of its fairest attainments ; that art should wither 
and literature decay ; that freedom of thought should become 
a crime ; that noble souls should rot in dungeons or agonise 
in flames ; that grown men should scream with the torture of 
the rack ; that whole peoples should be butchered ; that the 
riches of classical times should be piled in heaps and burned 
as impious. 

But the spectacle of history seems like that of nature. After 
a period of fruitfulness the field must lie fallow. A mighty 
creative effort is ofttimes followed by a long period of exhaustion 
and recuperation. Sometimes the human mind will spend all 
its energies in one splendid burst. So it seems to have been 
with Newton in the production of the Principia. One might 
imagine that the same thing might be true of the mind of the 
world. We shall perhaps not go wrong in believing that the 
period of Hellenic fructification came as a sort of climax to ten 
thousand groping years. As if the earth had borne too heavily, 
the seasons came, and with them the generation of men, empty- 
handed and without fruit, through a thousand or fifteen hundred 
sterile years. 

It is only in this vague wise, apparently, that we may picture 
the extraordinary eclipse which seemed to come over not merely 
the whole of Europe, but the whole of Western civilisation. 
It would be a mistake to suppose that this was merely the re- 
crudescence of paganism, or, again, that it was due merely to 
a triumph of religious fanaticism. The new faith of Europe 
was, it is true, but little more than a revival, with some addi- 
tions, of the old pagan cult. But in some sense the period of 
darkness had set in before the Church had gained its hold. 
Nero and the monsters of the purple preceded St. Augustine 
and the fathers. Imperial Rome was the penumbra ; Christian 
Rome was the full shadow. 

There has been in recent years a tendency to revive some- 
what the accepted picture of the Interregnum, to discover that 



152 THE WORLD MACHINE 

the Dark Ages were not so very dark, the fanatics of the Church 
hardly so maniacal as the earlier historians would have led us 
to believe. Doubtless there were some exaggerations, many 
inaccuracies. Gregory the Great may not have burned the 
Palatine Mbrary. In the monasteries some faint traces of 
ancient learning survived. A closer scrutiny wiU no doubt 
reveal some relief in the heavy lines of the now classical picture, 
drawn in the pages of Ranke, Draper, Llorente, Taine, and 
many another. 

But in general the attempt to rehabihtate what we term the 
Middle Ages resembles very much that sort of exaggerated 
reaction which proclaims the virtues of a Nero and the humanity 
of the misprised Tiberius. Let us not lose sight of the main 
facts. Freedom of thought was stifled. Natural inquiry was 
dead. The arts of civilisation all but perished. Sanitation, and 
with it civic decency, almost disappeared. The Paris of the 
twelfth century was a pig-sty. This was generally true of 
Europe, outside of the Arabian dominion, through eight or ten 
centuries. 

Great libraries were a characteristic of ancient civilisation as 
they are of modern ; one might almost call them an index. In 
the long Blight they were sacked, burned, and dispersed. At 
the close of the Ptolemaic dynasty it is estimated that the 
Alexandrian Library contained a total of 700,000 papyri. In 
the fourteenth century, when Charles V., surnamed The Wise, 
founded the Royal Library of France, he could amass 900 
volumes. He was a patron of learning, and so highly did he 
prize his collection that he had a catalogue made of it. So 
drear was the time that the fact has descended in its annals. 

The great collection of Alexandria was but typical of the 
age. It was begun by Ptolemy Philadelphus, successor of 
Ptolemy Soter, half-brother of Alexander the Great, who took 
for his portion the dominion of Egypt when the Macedonian fell. 
It was originally a part of the museum or university. The 
collection numbered 400,000 volumes when it was burned by 
Caesar. A second library estabhshed by Ptolemy Physcon in 
the great temple of Serapis, containing 300,000 volumes, escaped. 
To atone for the loss of the first, Mark Antony presented to 
Cleopatra the rival Hbrary which had been collected by Eumenes, 
King of Pergamus. The latter consisted of 200,000 volumes. 

What was true of the gay capital of the Greeks was almost 



I 



THE LEGACY OF THE GREEKS 153 

equally true of the Latin metropolis. As late as the fourth 
century of our era, it is said there were twenty-eight public 
libraries in Rome. One of these had been the fine Ulpian 
library, another that of the Palatine. Even in minor cities 
throughout the empire do we read of collections of considerable 
value and extent. 

Mournfully does the lover of books contemplate the fate of 
one and all. Three hundred years after the first destructive 
fire, the Alexandrian Library was pillaged, and in large part 
destroyed, by a wild rabble under the lead of the fanatical 
Bishop Theophilus, and countenanced by that Saint Cyril who 
instigated the atrocious murder of Hypatia. Three hundred 
years later still, its remnants were fed to the flames by order of 
the conquering Omar. Even then, so great was the number 
of papyri remaining, that, used to fire the baths of Alex- 
andria, it is recorded that six months were barely sufficient 
to consume them. An insane and burning hatred of learning 
seemed to inflame the heart of Christian and Mohammedan 
alike. Doubtless the great majority of these works were of 
mediocre value. Some few were not ; and to no man is it 
given to anticipate what will be held of most worth a thousand 
years beyond his age. It is with difficulty that he who reads 
now restrains his resentment against the destroyers of these 
interesting relics of the ancient mind. 

What the zealot left the hand of fate seemed to seize. The 
history of the libraries of Rome is a history of fires, which came 
as a part of the incessant conflagrations which visited the 
imperial city. Scant wonder is it then, that, suffering such 
adversities, so slight a portion of ancient literature should have 
come down to us, that the immensely larger part — more than 
ninety-nine per cent., we may imagine — should have been utterly 
and irretrievably lost. It hardly needs be added that the 
portion which appealed to the scholar and to the reading public 
least, that which dealt with the several sciences, should have 
been the most neglected and the least preserved. 

Of great libraries we hear no more until the rise of the 
Saracens and at the close of their era of conquest, along in the 
eighth and ninth centuries. Then it was that their more en- 
hghtened Khalifs began again the sedulous hoarding of books. 
Al-Maimun, son and successor of the distinguished Haroun 
Al-Raschid, is reported to have brought into Bagdad hundreds 



1 54 THE WORLD MACHINE 

of camel-loads of manuscripts. The spirit of collection eventu- 
ally extended over the whole empire. Its rival divisions vied 
with each other in their accumulation. The Fatimite Library 
at Cairo numbered, it is said, 600,000 volumes — figures which 
may be taken perhaps with some reserve. Yet its catalogue 
alone was said to occupy forty-four. In Andalusia— that is to 
say, in Mohammedan Spain — there were seventy public libraries 
recorded. The collection of private individuals was often ex- 
tensive. A modest physician Draper reports as having refused 
the invitation of a Sultan of Bokhara because the carriage of 
his books would have required four hundred camels. 

Retribution for their evil deeds in the earlier time fell upon 
the Mohammedan when the hordes of Christendom swept 
through his dominions. A great library at Tripoli was burnt 
by the Crusaders. It was fancifully said to contain three 
million volumes. When the Moors were driven from Spain, so 
the story runs, the Cardinal Ximenes made a bonfire in the 
squares of Granada of 80,000 Arabic manuscripts, many of them 
translations of classical authors The position of the nations 
had become strangely reversed. The aforetime foes of learning 
had become its protectors. The legitimate heritors of the Greek 
tradition had become its implacable enemies. 

The Saracenic civilisation, indeed, presented a singular 
contrast to the sodden and seemingly irretrievable stagnation 
which had settled upon the rest of Europe. By a curious and 
violent paradox, the like of which has seldom been known, a 
fierce, ignorant, and warlike race, dominated by as intolerant 
a religion as perhaps had ever been known, became the con- 
servators of such science and such knowledge as yet remained 
among men. They had not merely libraries ; the empire was 
dotted with colleges, with great universities and medical schools. 
The first of the latter established in Europe was said to have 
been that of the Saracens at Salerno in Italy. The first 
astronomical observatory was that erected by them at Seville 
in Spain. 

The order of culture that obtained for a time among the 
Saracens was high. For two or three hundred years, from the 
time of the Khalif Al-Maimun, the wide area from Samarcand to 
Fez and Cordova was the theatre of a rich and varied life. 
Letters were again cultivated ; a taste for the classics was 
revived. All the stores of ancient learning were exhumed, were 



THE LEGACY OF THE GREEKS 155 

translated, and subjected to exhaustive commentary. The 
measure of the earth was again undertaken. Astronomy again 
found high favour. Men of learning were again held in honour. 

The making of books became a trade. In Bagdad, Honian 
set up the earliest publishing house of which we know. The 
study of mathematics was again ardently prosecuted, our 
modern algebra developed. 

Famihar Omar Khayyam may serve as a type of the time. 
He seems to have been a singularly accomplished and gifted 
man. He was by profession a mathematician and an astronomer, 
wrote a treatise upon algebra, calculated elaborate astronomical 
tables, still of value, and reformed the calendar. This was at the 
command of the Sultan, Jalal-u-din, and his chronology was 
known as the Jalali era. Gibbon refers to it as " a computa- 
tion of time which surpasses the Julian and approaches the accu- 
racy of the Gregorian style." It will be recalled that he was the 
friend in youth of Al-Hassan, a powerful and evil genius, who 
became the founder of the famous and infamous sect of the 
Assassins. With Hassan he rose to high favour at the court, 
and as he seemed to covet little and enjoy much, he must have 
passed an unwontedly serene and agreeable existence. The 
ancient chronicles refer to him as " The King of the Wise," 
" in science unrivalled, a very paragon of his age." His poetry 
must have been a diversion ; he seems to have been one of 
the rare instances known to literature of an intellect of a really 
high order, commanding the full knowledge of his time, and 
united with a true poetic gift. Beside him Lucretius and Goethe, 
in a more restricted sense Tennyson and Leconte de Lisle, are 
among the few conspicuous examples which could be cited. 

Omar was not merely a poet and man of science ; he was a 
philosopher as well. His tenets perhaps most resembled those 
of Epicurus. With the latter he might have inscribed over the 
door of his garden the legend reported by Seneca : Hospes hie 
bene manehis ; hie summum bonum voluptas est{" Tarry, stranger ! 
here pleasure lords the day "). But on the whole he was not so 
much an Epicurean as a complete hedonist. His philosophy of 
life bore as much resemblance to the chaste and reticent stanzas 
that FitzGerald fashioned for the edification of young minds of 
both sexes as the life and teachings of Sakya-Muni to the late 
Sir Edwin Arnold's beguihng romance in verse. He was a 
frank sensualist, and as utter an infidel as ever roamed the 



156 THE WORLD MACHINE 

highways of human thought. In this, if we may judge from the 
unaffrighted impudicity of the prevalent Hterature and chronicles, 
he represented perhaps better than any other the cultivated 
Arabian spirit of the eleventh and twelfth centuries. 

But if this ardent and somewhat fanatic people could pro- 
duce genius of so high an order and sense of so rare a make, 
if it could reach a stage wherefrom it could brook without dis- 
quiet so candid a denial alike of morality, faith, and the 
solemnity of life, its limitations were still sharp. 

The character of the Saracen resembled much that of the 
faithful servant entrusted with the one talent, who carefully 
treasured it in the earth until his master should come again. 
If they preserved much, they added httle. If they became the 
heritors of Greek culture, in no notable degree did they imbibe 
the Greek spirit. On the more serious side they displayed but 
slight originality. They copied ; they transcribed ; they made, 
as it were, copious notes. But a genius for independent inquiry, 
for new synthesis, they nowhere displayed. They produced 
encyclopaedic works ; but of such a type as those of Pliny 
and Aristotle. Indeed, the formal mind of Aristotle, with its 
extraordinary miscellany of information, its empty definitions, 
its unfruitful classifications, represents fairly well the intel- 
lectual level of this very remarkable race. Al-Hazen, Ibn Junis, 
and their kind did better, did real things ; but Averrhoes, 
Avicenna, and their like thought and wrote after the manner of 
the Greek mind before it had developed its genius for measuring, 
for weighing, for computation, and for daring induction. 

This characteristic was by no means insular to the Saracen. 
It was shared equally by Bagdad and Byzantium, by Paris as 
by Cordova. The worship of Aristotle — for it was no less than 
that — was indeed one of the most curious phenomena of this 
enigmatical time. InfaUibiHty was attributed to his works in 
hardly less a measure than to the Hebrew scriptures. To 
doubt them, among the more northerly peoples at least, was 
impious. In England and in France there were statutory 
enactments which made it a crime. 

Moreover, in no wise did the Saracen mind ever attain to 
that complete intellectual freedom which was the characteristic 
of the Hellenes. They were weighted with the cult of a gloomy 
religion as Europe was weighted. They bore it more success- 
fully. Their cleanly and ofttimes beautiful cities, their magni- 



THE LEGACY OF THE GREEKS 157 

ficent palaces, their splendid libraries, their literature, their 
restless and inquiring, if still somewhat subjugated spirit, amply 
attest the fact. They made some progress in their physical 
investigations ; in some sense they transformed alchemy into 
a science. Many of our scientific terms are transferred directly 
from their language. 

But there was something in their mental organisation or 
something in the time which held them in check. We may not 
inaptly compare them to the Hindu or to the Chinese. Our 
decimal notation is an evidence of the success with which the 
Hindu cultivated mathematics. We know that the Chinese 
possessed the compass a thousand years before our era ; the 
printing-press and gunpowder yet more anciently. Yet with 
the aid of his more facile methods of calculation the Hindu made 
no contributions worthy of his invention. With the printing- 
press the Chinese spread wide no wonderful literature. By the 
aid of the compass they made no great discoveries. With the 
aid of gunpowder they made no vast conquests. Neither 
Chinese nor Hindu made any notable additions to the stock 
of human knowledge. They left no deep impress upon human 
civilisation. They made interesting beginnings, then stopped. 
The same is true of the Saracen. 

Doubtless, if the arms of Charles the Hammer had not stayed 
the northern sweep of the Mohammedan hosts, the six or seven 
centuries of European history that followed would have been 
written in far different fashion. It is scarcely believable that 
they could have fixed their faith upon the North. It is scarce 
believable that their yoke would have remained for long. But 
in the clash of warring creeds, in the mingling of alien peoples, 
in the diffusion of Arabian culture, the reintroduction of the 
manners and modes of civilised life, the utter stagnation which 
had fallen upon European lands, we may believe, would have 
come to an end. We may conjecture that from this foreign in- 
vasion might have resulted something of that same freedom 
and stir of life which came with the struggle of the sects in 
the Reformation, eight centuries later. 

It was not to be. The tide of the Saracen was rolled back- 
wards, its energies of conquest were turned into the channels 
of intellectual development. Europe was left to rot on, until 
in the obscure order of events, time for it should be born 
again. 



158 THE WORLD MACHINE 

There are in the history of the last twenty centuries two 
events of incomparable interest. The one was the extinction 
of Hellenic civilisation ; the other was the Renaissance. Per- 
haps at a later day, when history has ceased to be a babbler's 
chronicle, the causes which resulted in these two momentous 
events will be divined, and we shall understand the periods 
of ebb and flood of the human mind as accurately as we now 
follow the waters of the ocean. As yet they are profoundly 
obscure. We may remark the introduction of gunpowder ; 
but gunpowder was apparently known in some form to the 
Greeks, and throughout the whole of the dark time. We may 
consider the printing-press ; but the printing-press merely 
substituted the turning of a wheel for the hands of forty slaves. 
We may note the incoming of the compass ; yet it is not im- 
probable that the compass, too, was obscurely known to the 
Greeks, and that through travellers and conquerors who may 
have come in contact with the peoples of the East it might 
have been imported at any time within, say, fifteen centuries 
before its use became general. 

We may prattle of the fall of Constantinople, the incursion 
of Greek scholars into Italy, and the ensuing revival of a taste 
for ancient letters ; but there is no evidence that the study 
of Greek was ever wholly banished. And when we have idly 
enumerated these inconsequent and insufficient " causes " we 
are no forwarder. 

We cannot comprehend why it was that after a splendid 
fruitage the vineyards should wither and their bearings cease. 
We know as little why it was that after so many weary and 
hopeless years the seed should spring again from the ground 
and a new and vigorous life come again to men. Perhaps the 
atmosphere of freedom and enlightenment in the earlier time 
brought a kind of intoxication which ended in debauchery and 
excess. Something of the sort appears obscurely to have been 
the case. When the removal of every restraint to their power 
bred madmen for emperors, Rome became less a capital than 
a lupanar. 

Certainly there seems to have ensued a period of weakness 
and exhaustion, and perhaps we may regard Christianity as a 
sort of a fever which, in its period of weakness and exhaustion, 
seized upon the race. 

This fever had to run its course. We know that in the end 



THE LEGACY OF THE GREEKS 159 

it produced something of that same sense of aridity and de- 
pression and a sterile and profitless atheism which came to 
the earlier day. Faith crumbled, we know not why — perhaps 
more from physiological than intellectual reasons. Religion 
ceased to satisfy men's needs, and the new Evangel had not 
come. At the end a pope, Urban VIH., wrote upon the tomb 
of his brother : Hie jacet pulvis et cinis ; postea nihil ; " dust 
and ashes, and in the after — nothing ! " 

But even while this disillusioned pontiff, like another Cohelet, 
or whoever may have been the author of Ecclesiastes, was thus 
writing down the vanity of life, the futility of human concerns, 
to the world about him a marvellous awakening had come. 
It had come subtly, unobtrusively, without that any man knew 
why, or that the most of men were aware. At the opening of 
the qiiattro cento, into a cup of exquisite chasing Dante had 
poured the alembic of the new Italian tongue. Fleeing before 
the invading Turk, the exodus of the pedants into Italy had 
brought resurrection to the immortal works of Greece. 
Petrarch and Boccaccio, fired with enthusiasm for the new 
study, had made ancient learning again the fashion. From 
Marco Polo, from Mandeville, and other travellers had come 
dazzling tales of unknown lands. The spirit of adventure 
stirred anew. 

At the same time trade and commerce were flourishing as 
they had not flourished in centuries. The northerly lands of 
Europe were becoming rich. To the leisured class came time 
to learn, and with it the vanity to affect tastes and cultivate 
aptitudes which lifted them yet a little further from the crowd. 

The intellectual movement was widespread. The introduc- 
tion and prevalent use of gunpowder resulted at last in a demand 
for a theory of explosions. A mingled chemistry and alchemy 
had been imported from the Moors. The zest for inquiry ran 
into channels the most diverse. In Leonardo da Vinci was 
incarnated one of those multifarious minds which appear once 
in a century or more. Painter, poet, engineer, strategist, in- 
ventor of canal locks, a student of shells and stones, of plants 
and trees, of pigments and the effects of light, he became the 
founder of half-a-dozen sciences. 

To still larger results, in the far-off wilds of Great Britain, 
in the solitude of the cloister, and persecuted as a necromancer, 
Roger Bacon had toiled at the resuscitation of physical science. 



i6o THE WORLD MACHINE 

His works, filtering through the pens of Cardinal d'Ailly and 
others, caught at last the ear of a strange and masterful man, 
a wanderer and a thinker, half a pirate and half a seer ; and 
out of the tumult of his ideas came at last the project of a 
voyage to India through the waters of the unknown west. The 
mystic needle which would pilot the mariner without the aid 
of headland or star had come into general use. Adventurous 
voyages were being undertaken. An era of maritime discovery 
had been begun. The circumnavigation of Africa was to be 
attempted anew. From one of his most distinguished country- 
men, the Florentine astronomer Toscanelli, Columbus had found 
reassurance for his great design. The ancient speculations of 
Eratosthenes and Strabo as to the feasibility of such a voyage 
and the existence of other and doubtless habitable continents, 
were being ardently discussed. For a century or more these 
ideas had been revivified and popularised through the curious 
and widely read writings of Sir Jehan Maundeville, " Knight of 
St. Albans." 

The mistaken measures of the circle of the earth handed 
down from Ptolemy, the equally mistaken ideas as to the distance 
of India to the East, gave to the project a far less hazardous 
air than the reaUty would have presented. StiU. it was difficult 
enough ; in the minds of most, a fantastic dream. 

The discovery of the New World came to Europe like a 
bolt from the blue. Yet the quest of Columbus was in some 
sense as definite an inquiry as a laboratory experiment. Measure- 
ments had been undertaken ; a fund of fact and theory had 
been evolved ; vast inductions had been framed. The prows of 
the Santa Maria and its companion vessels were turned towards 
the west to test the vaHdity of these conceptions. It was 
experimental science put to the proof. With the news of the 
discovery the enlightened spirits among mankind saw, as it were, 
in the skies a sign — 

"In hoc signo vinces." 

The scientific method, the rational use of experience, of in- 
ference from careful observation, of hypothesis and verification, 
had won its first brilliant victory in the new time. The march 
of the mind towards the intellectual conquest of the world — 
destined, we may believe, never again to be interrupted or 
thrown back so long as the human race survives — had begun 
again. 



CHAPTER XIII 

COPPERNICUS; THE TRUE SYSTEM OF 
THE WORLD 



If there be some babblers who, though ignorant of all mathe- 
matics, take upon them to judge of these things, and dare to blame 
and cavil at my work, because of some passage of Scripture which 
they have wrested to their own purpose, I regard them not, and 
will not scruple to hold their judgment in contempt. 

CoppERNicus, De Revolutionibus {Dedication to the Pope). 



CHAPTER XIII 

COPPERNICUS; THE TRUE SYSTEM OF 
THE WORLD 

If we search the later annals of mankind for its most pivotal, 
most momentous event, we shall mark beyond doubt the voyage 
of Columbus. There is no other single fact, no circumstance, 
no happening, so fraught with vast issue. Its effect upon Europe 
was simply dramatic. After the three thousand, live thousand, 
years known to history, after perhaps ten or twenty thousand 
years of timid groping, of piece by piece conquest and discovery, 
wherein a chance wind or storm may have played the ruling 
part, the ranges of the earth were suddenly doubled. In ten 
or twenty years they had been extended thirty or forty fold ; 
the ships of Magalhaens effected an actual circumnavigation 
of the earth. The truth that it was a globe had been experi- 
mentally and irrefutably demonstrated. Europe began again 
to think, to wonder, to reason. 

The ferment was profound. The heart of the world was 
aflame with a lust for gold, with a fever of conquest, with a 
passion for discovery, with a longing to see, to explore, to know. 
For centuries, for near a thousand years, the chief external 
concern of the great body of humankind had been their souls. 
Their speculations touched the nature of God, the remission of 
sin, the life to come. Their thoughts turned suddenly towards 
the new Indias beyond the sea. It was as if the curtain had 
been drawn aside upon some wondrous prospect, some theatre 
of the unimagined, the unsuspected, the unknown. Kings 
dreamed of new empires ; to the peasant in the fields, to the 
monk at his orisons, the scholar in his cloister, the spinner card- 
ing his wool, came the vague stir of a larger life. 

The ferment, at first a confused awakening of new impulses, 
new ideas, speedily became moral. Within twenty years of 
Columbus' voyage, Luther had nailed his theses on the cathedral 

door of Wittenberg ; in an age of universal submission to 

163 



i64 THE WORLD MACHINE 

authority a blow for the right of private judgment, the Hberty 
of the human conscience, had been struck ; the long struggle 
against the benumbing yoke of an all-powerful ecclesiasticism 
had been begun. Servetus, Vanini, Bruno had yet to go to 
the stake ; but the term of religious persecution, which the 
careful and unimpassioned Ranke estimates had cost Christendom 
ten million victims, was approaching its end. 

With this moral revolt came a kindred awakening of the 
intellect. Ten years after the outbreak of the Reformation, 
Jean Fernel, a French physician, made the first measure of the 
earth, so far as we know, on European soil. Twenty years 
before him, a Roman Catholic priest, in an obscure corner of 
Poland, had begun upon a work that, by a favouring accident, 
was destined to accomplish a greater revolution in the thoughts 
of men than any single volume before or since. 

Nicolaus Coppernik's book on the Revolution of the Heavens 
did not see the light until the year and near the day of his death 
— that is, in 1543. In his dedication he records that he had 
been at work upon it for nearly forty years. He was a fearless 
thinker, but doubtless he loved his peace of mind, and Europe 
was then a vast holocaust of heretics. The papal Inquisition 
had been established when Coppernicus was a boy ; Llorente, 
its historian, figures that in eighteen years Torquemada and 
his collaborators had burned ten thousand victims, and tortured 
and punished a hundred thousand more. 

Coppernicus dedicated his book to the Pope ; he had been an 
instructor in mathematics at Rome, his uncle was a bishop, and 
his feeling about the sort of criticism his book would meet is 
shown well enough in the lines that preface this chapter. But 
still he did not dare. A cardinal became its sponsor, and the 
frightened Osiander, who put it through the press, wrote for 
the book a foreword in Coppernicus' name, exhibiting it as 
simply an hypothesis, this motion of the earth. What a state 
of the world ! 

Whoso reads now the De Revolutionihus will close its pages 
with mingled feelings. So far as mere facts go, there was not, 
to speak strictly, a great deal in it, of value, that was wholly 
new. A great deal of it — six of the twelve chapters of the 
first book, for example, and much of the rest — ^was little more 
than an abstract and commentary of the Almagest of Ptolemy 
of Alexandria. Coppernicus was an exact and Hfelong observer 



COPPERNICUS 165 

yet there is little in his work that could not have been, and 
probably was not known to Ptolemy and Hipparchus. His in- 
struments were, of course, the same ; he had his unaided eyes 
to see with, as did they — nothing more. He can hardly be 
said to have made any great discovery — possibly one ; nor did 
he bring forward many new and decisive facts. He met objec- 
tions to his theory in the same way that Aristarchus had ; his 
arguments were the same. He can estimate no better the 
distance or the grandeur of the sun, the moon, or the stars. 

This seems rather sweeping and assuredly caviare to the 
general view. In most popular accounts you will find it stated 
that " Coppernicus did not merely speculate, he proved " that 
the earth was a planet like the rest, and revolves about the 
sun. The general opinion of astronomers is otherwise. We 
have it in the words of the learned Schiaparelli that — 

" The two systems (the Ptolemaic, which reigned so long, 
and the Coppernican) could be adapted to represent the pheno- 
mena of the heavens equally well ; geometrically, they were 
equivalent between themselves, and likewise to the system of 
Tycho. Even Kepler, with his ellipses, was not able to over- 
come the possibility of sustaining the immobility of the earth. 
It was only Galileo and Newton who, setting out from physical 
principles better grounded than those up to that time dominant 
in the schools, were able finally to overturn it." ^ 

In truth, the absolute demonstration did not come until the 
middle of the nineteenth century. Why, then, does the work 
of Coppernicus in some sense mark an epoch in the history of 
human ideas ? 

First of all, because it turned out to be the truth, to portray 
the unbelievable reality ; but as much more because it is among 
the highest products of the imaginative faculty. You will read 
in many a place that Coppernicus was not a great and original 
genius, in the sense that Newton and Darwin were. With all 
that he borrows from Ptolemy, a careful study of his work 
assuredly gives one a different impression. Consider that he 
lived in an age when astronomy and astrology had not parted 
company, and that amid all the wild fancies then prevalent 
you find it a sane and modern work. Very often its mode of 
reasoning is not satisfying ; you meet at times with the same 
empty verbal explanations, as that the earth is round " because 
^ / Precursori di Copernico neW Antichita, Milano, 1873. 



1 66 THE WORLD MACHINE 

a sphere is the most perfect form," &c., which is characteristic 
of Aristotle and the ancients. But it bore no trace of that 
errant-minded mysticism from which even Kepler in the next 
century had not freed himself. 

For the rest, it is written in such a straightaway, calmly 
confident manner that, knowing how nowadays, and in the old 
days too, successive works of science are as a rule little more 
than compilations from some previous work, you might readily 
suppose a high state of astronomical science in his time. We 
know, of course, that it was full of the wildest fancies, that 
almost anybody's guess found credulous attention. 

Despite the faint-hearted preface inserted by other hands, 
Coppernicus does not in the least put forward his ideas as a 
mere hypothesis. He believes in them serenely, proves them 
to his own satisfaction, and, more curious still, for any alterna- 
tive suggestions has only the scantiest word. He does not 
sketch out the old Ptolemaic ideas so long in vogue ; he goes 
straight to his task. First of all, the world — that is, the whole 
cosmos — is a sphere. This takes only ten lines to prove. The 
sphere is the most perfect form. It is evident that the heavenly 
bodies are spherical, just like a drop of water, therefore the 
heavens too must be spherical. 

This is logic that limps, and, coming on the earliest page, 
it gives you an unfavourable impression. It is almost the 
weakest point in the whole book. In the next chapter he details 
all the familiar reasons to prove that the earth is likewise a 
sphere. He points to the discovery of America as further proof, 
and it is evident that this central fact had taken a strong hold 
upon his mind. 

In another section he goes on to prove that the motion of 
all heavenly bodies must be in a circle. We know he was 
wrong here, but in this assumption he dismissed the clumsy 
system of epicycles of Hipparchus and Ptolemy. Then he 
plunges abruptly into the question of the motion of the earth. 
Since it has been shown that the earth has the form of a globe, 
it is now in order to inquire whether, from this fact, it does not 
also possess a motion ; likewise what place it occupies in the 
universe\ Most writers, he says, agree that the earth is the 
middle point of the world, and find any other suggestion not 
only inconceivable but laughable. Coppernicus does not. He 
has been pondering the matter for forty years, and has set 



COPPERNICUS 167 

himself free, at last, from the bondage of appearances. He 
offers a simple demonstration of the infinite range of the 
heavens, which has already been sketched on a former page.^ 
He very briefly outlines the ideas of the ancients, then sets 
himself to disprove them. You turn the leaf, and with no flare 
of trumpets, hardly an air of novelty, you find a chapter inquiring 
whether or no the earth has not one motion, but several. 

You reflect that this is a work which turns the world upside 
down. You have somehow the idea that the proof should be as 
long and detailed as Darwin's demonstration of natural selec- 
tion ; instead, the subject is swiftly compassed in a few pages. 
The next chapter sets out the order of the planets. Then comes 
the final section of the first book, wherein Coppernicus sets 
forth what he calls the third of the earth's motions. This last 
alone would have entitled him to a high rank among astrono- 
mical discoverers, yet he gives it simply as a part of his system, 
without any ado, making no note that it is wholly and en- 
tirely his own. You perceive how carefully and patiently he 
has thought his subject out and woven it into a firm and 
connected piece. 

In the expression of his ideas regarding this third motion, 
Coppernicus was unfortunate. To account for the changing 
seasons, the varying length of the days, he speaks of a " motion 
of declination," as though the tilt of the earth's axis to the plane 
of its orbit were variable throughout the year. Hence he 
assumes a motion of the axis. We know now, of course, that 
the assumption was needless. There is no annual motion as 
he thought ; the tilt remains very nearly invariable. But, in 
following out this idea of a changing inclination, he got sight 
of the real sway of the axis, and works it out clearly ; though, 
of course, he could not at that day divine the cause, nor, 
geology unborn, could he surmise the effect. 

Every school student of astronomy knows what this third 
motion was. Hipparchus and others had made it clear that 
what we call a year falls a little short of making a complete 
circle of the heavens, that the sun seems to move a little in 
its position, say, from one spring to another. This gives rise 
to the so-called precession of the equinoxes. That there was 
some such a shift there could be no question ; it was an in- 
contestable fact ; but there was no theory to account for it. 
1 " The Ideas of Aristarchus," p. 113. 



i68 THE WORLD MACHINE 

Cappernicus saw that if the earth in its cirding round about 
the sun did not hold always to exactly the same tilt, that if 
its axis swayed ever so little, this would produce precisely the 
effect noted. He works it out, writes the very briefest descrip- 
tion of it that he may, gives you a diagram to make it all 
perfectly clear, then goes on his way. He may have disclosed 
his discovery to some of the enthusiastic young men who had 
heard a rumour of the new teachings and came to ask con- 
cerning them. Beyond this, there is no evidence that he ever 
wrote a line about it outside of the work which immortalised 
his name. 

But consider what it all meant. Not only had he seen with 
the Pythagoreans that we must conceive the earth as slowly 
turning on its axis ; not only had he reached the far more 
difficult point of view of Aristarchus, that the earth swings in 
a vast circle about the sun ; but he had in his mind's eye pictured 
this vast globe careening slowly as it sweeps along the plane 
of its colossal orbit. Consider that he had no miracle-working 
telescopes with which to search for demonstrations of his ideas, 
nor to bring to his notice curious appearances that might 
suggest these ideas to his mind. He had such eyes to look 
upon the heavens as you or I, no more ; but he saw with that 
inner eye, with that inner sense, that we call imagination. Con- 
sider that he wrought alone, that he had to dig his very founda- 
tions himself ; consider that he made no part of a brilliant 
school of astronomers, thinkers, philosophers, as at Alexandria, 
but that he followed through his simple and exemplary life in 
a lonely corner of Poland, far removed from the stimulating 
plaudits of the world, and we shall not go far wrong perhaps 
in reckoning him, in power of abstraction, as among the greatest 
of mankind. 

The more important part of his work is summed up in the 
fifty pages which comprise the first of his six books. The rest 
of them is devoted patiently to working out in all their detail 
the conclusions he had reached. He discusses the inclination 
of the ecliptic, the equinoxes, the solstices, and makes clear the 
intimate mechanism of nights and days. He goes deeply into 
the revolutions of the moon, its variations, its inequalities ; 
discusses in this connection its distance and size, and the 
distance and size of the sun ; getting no further, as we have 
seen, than had the old Alexandrians so long before him, never- 



COPPERNICUS 169 

theless fixing clearly in the mind of the reader that a simple 
way exists to measure these distances and magnitudes, and 
that this is all a part of the solid chain of his theory. 

In the fifth book he sketches the placing and the motion of 
the planets, determines their relative distances, and for the first 
time in history, so far as we know, the human eye has seen 
the world machine in motion, just as it is. True, he does not 
see it whole ; he knows nothing, of course, of the two outer- 
most planets, Uranus and Neptune. He knows nothing of the 
asteroids, of the '* shattered planet " ; he knows nothing of the 
moons of Jupiter, and neither for him nor for any man for a 
long time after do the comets come and go in obedience to 
natural law. 

But such of it as his unarmed eyes could see, he saw true. 
For the first time, so far as we know, all of the known planets 
were set in their true position, with the sun at their centre of 
motion. Some of the ancients, Apollonius of Perga perhaps, 
had correctly pictured Mercury and Venus as satellites of the 
sun. Aristarchus, in picturing the motion of the earth, must 
have conceived the moon describing its epicyclic motion about 
the moving earth, and having caught the truth so near, he may 
have seen it all ; we do not know. If he left any treatise other 
than the slender brochure which has come down to us, it is 
lost. More sheerly than it has been given to many great dis- 
coverers in the history of science, Coppernicus' vast theory 
was his own. 

He quoted little ; he showed, indeed, a kind of aloof in- 
difference to the opinion of friend or foe. He must have cared 
but slightly for applause. He seems to have shared something 
of the old Pythagorean idea that the truth was for the elect 
alone. It was his original intention to communicate his theory 
only to friends. You catch a little of his spirit when he refers 
to Lactantius, " who had spoken so childishly of the form of 
the earth, deriding those who held it to be spherical." He 
observes : " On mathematical subjects one should write only 
to mathematicians." His style is simple, homely, direct. Occa- 
sionally you feel that his quiet pulses might, in Tyndall's phrase, 
have been the seat of a nascent thrill. Defending his helio- 
centric arrangement of the planets, there is a passage which 
runs : — 

"By no other arrangement have I been able to find so 



170 THE WORLD MACHINE 

admirable a symmetry of the universe and so harmonious a 
connection of orbits as by placing the lamp of the world, the 
sun, in the midst of the beautiful temple of nature as on a 
kingly throne, with the whole family of circling stars revolving 
around him." 

It is the mediocre imagery of a simple priest. For the rest, 
he speculates little : he is content to describe ; he does not 
guess. His mind was that of a geometer. He does not try 
to seek out causes which lie at the base of this wonderful scheme 
whose secret he has at last penetrated. The force which moves 
the planets, which so tormented the mind of Kepler, did not 
trouble his. Some attempt has been made, by Humboldt among 
others, to show that some crude notions he had of the force of 
gravitation. There is a passage with these rather striking 
lines : — 

" The earth cannot be regarded as the middle point of all 
these planetary motions ; that is apparent from the unequal 
and variable movements of the planets themselves, and from 
their varjdng distance from the earth, which cannot be explained 
by means of concentric circles with the earth as a common 
centre. Inasmuch, now, in this view, several middle points 
would necessarily exist, so no one can be in doubt as to whether 
this middle point of the world be that of terrestrial gravity, or 
elsewhere. I at least hold to the view that gravity is nothing 
else than a natural inborn endeavour impressed upon every 
particle by the divine providence of the Master of the universe, 
whereby these particles tend to coalesce into the shape of a 
sphere, and thus gain their unity and wholeness. And it is 
to be supposed that this inclination or tendency dwells also in 
the sun, the moon, and the other planets, and it is to this cause 
that the spherical form in which they appear is due, while they 
nevertheless in varied fashion cruise about their orbits." ^ 

The passage is interesting as a curiosity ; it is evident enough 
from many another that the idea of the sun as an attractive 
centre was wholly foreign to his thought. He does not seem 
to have been interested in the speculations of the ancients. The 
ideas of Anaxagoras he does not mention ; neither those of 
Simplicius. There is nothing in the mental habit of the time 
to impel him to think upon such matters at aU. Machines, 
mechanical arrangements of any sort, were almost wholly lack- 
1 De Revolutionibus, Book I. chap. ix. 



COPPERNICUS 171 

ing in his day. Men could hardly construct a mechanical theory 
of the heavens before they had felt the need of a mechanical 
explanation of the simple facts of their daily lives. 

These were his limitations — the natural limitations of his 
age. They should in nowise detract from the just measure of 
his strength. He achieved a lasting work. This comes to few. 
It was enough. 

He died as he had lived, in far-away Poland, seven years 
after Erasmus, three before Luther, while Henry VHI. ruled in 
England and Francois Premier in France, and while the Medici 
still moulded the brilliant life of Florence. No doubt he died 
content — content and convinced ; but neither his death nor 
his book made any stir. He wrote, of course, in Latin ; his 
book seems never to have been translated into any other tongue 
until the four hundredth anniversary of his birth. It could 
not be read by the vulgar. The lives of men went on just as 
before. There is little evidence to show that any one dreamed 
that he had exploded a bomb-shell. It was just seventy-five 
years before the Church thought enough about the matter to 
ban his book from Christian eyes. How came it, then, that 
his ideas were not to live a little, then to be forgotten, like those 
of Aristarchus, for another eighteen hundred years ? 



CHAPTER XIV 

BRUNO AND THE RECEPTION OF THE 
COPPERNICAN IDEAS 



Thoughts that great hearts once broke for 
We breathe cheaply in the common air. 

The dust we trample heedlessly 

Throbbed once in saints and heroes rare, 

Who perished, opening for the race 
New pathways to the common place. 

Lowell, Masaccio. 



CHAPTER XIV 

BRUNO AND THE RECEPTION OF THE 
COPPERNICAN IDEAS 

In the fifteenth century chance shook from its box of miracles 
another wonder than the discovery of the New World, hardly 
less fateful in its effects. That was the printing-press. It is 
with an ineffectual effort that we endeavour to realise now 
what was the world like when it had no printed bulletins of 
happenings on the earth, no chronicles and reviews for the easy 
dissemination of ideas, impressions, discoveries ; no means for 
the rapid duplication of a book. 

If now we look back into this time, we shall see how vitally 
separated were the conditions under which Aristarchus in 
Alexandria, Coppernicus in Frauenberg, wrought. The work of 
the Polish innovator was printed. A little later yet another 
invention was to confirm, for all time, their common idea. There 
seems little to doubt that, alone, the introduction of the 
printing-press into Europe would have saved the system of 
Coppernicus from the fate of that of his forerunner in Alexandria. 
It was not so much the mere preservation of the printed 
word. The papyri upon which the ideas of Aristarchus were 
inscribed will last longer probably than any work of paper and 
print. The employment of slaves as copyists ensured a tolerable 
circulation for any work of note. We know that they had vast 
libraries ; there were booksellers in that day as in this. Never- 
theless, prodigious as was their industry, the hand could not 
compete with the machine. The price of books even in 
Alexandria was exorbitantly high ; they were the treasures of 
rich men and kings. 

With the coming of the printing-press, says Draper, the 
price of books was reduced by four-fifths. The use of electricity 
in our time has not spread more swiftly than did the printing 
art in the first thirty or fifty years after Gutenberg and Coster. 
Between the years 1470 and 1500 more than ten thousand 



176 THE WORLD MACHINE 

editions of books and pamphlets were printed. You realise, 
then, how it was that the discoveries of Columbus, of Da 
Gama, of Magalhaens were so soon the common property of 
all Europe. You realise that of the thousand " reformations " 
which had been started in the thousand years of the ascendency 
of the Church, it was Luther's, in the second decade of the 
new century, which could make head, which no papal power 
could stay. You realise that it was a changed world into 
which, twenty years later, the work of Coppernicus was born. 
The habit of books, the habit of reading, was spreading fast. 

Still, his disciples were few enough. There was, while he 
lived, a young professor of mathematics in the University of 
Wittenberg, Rheticus by name, so eager to know more of the 
new ideas that he travelled to Poland to sit at the master's feet. 
It is evident that even then reports of Coppernicus' theories 
had begun to circulate. As early as 1536, from far-off Capua — 
and Southern Italy was a long way off then — the Cardinal 
Schonberg had written to him, saying : — 

" I learn that you have established a new system of the 
world, according to which you teach that the earth moves ; that 
the sun occupies the deepest and, therefore, the middle place 
of the world ; that the true heavens remain immovable and 
eternal ; and that the moon, together with all the included 
elements between the heaven of Mars and that of Venus, turn 
in their yearly course about the sun. I hear that you have set 
forth your entire system of astronomy in a commentary ; that 
you have gathered up the carefully reckoned movements of the 
planets into tables, to the profound wonderment of aU who 
have seen. Therefore do I beg you, most distinguished scholar, 
that you communicate to the instructed among men your dis- 
coveries, and that you will send to me as soon as possible your 
nightly labours over the structure of the world, together with 
the tables and anything else that you may have." 

He sends this by messenger, with money to defray all ex- 
penses, so keen is the cardinal to learn of the new Word. After 
the book had appeared, it found defenders here and there. 
Rheticus teaches it at Wittenberg ; Michael Moestlin inculcates 
it at Tiibingen. It is his largest claim to fame that it was under 
his influence that the mind of Kepler was formed. In England, 
Gilbert of Colchester, physician to Queen Elizabeth, founder of 
the new sciences of magnetism and electricity — he, indeed, who 



BRUNO 177 

coined the latter name — becomes its hearty advocate ; he ex- 
pounds the evidence in its favour with sobriety and force. 

But it is evident that the new scheme of the world took hold 
slowly. When Galileo gets into correspondence with Kepler, 
at the close of the century, he tells his new-found friend that 
he " has long been a convinced Coppernican " — evidence enough 
that there are very few who are. The greatest observing 
astronomer after Coppernicus, and the greatest scientific figure 
in Europe, Tycho Brahe, sets his face against the new doctrine. 
It is Tycho's accurate and admirable observations which guide 
Kepler's hands in the perfectioning of the Coppernican ideas ; 
yet he will remain unconvinced so long as he lives. So will 
the other great figure of the time, Lord Bacon, even though 
he lives long enough to know of all of Galileo's discoveries ; and 
the heavy, peasant mind of Luther, in daily active combats 
with the devil, could see in Coppernicus only " an upstart 
astrologer," " a fool who wishes to overturn the whole science 
of astronomy." " Does not the sacred Scripture tell us that 
Joshua commanded the sun to stand still, not the earth ? " 
Even Leonardo da Vinci, as myriad-minded a genius as ever 
lived upon this earth, born nine years after the De Revolutionihus 
had come from the press, pioneer in half-a-dozen sciences, 
interested enough in astronomy to figure out that the dim figure 
of the whole moon seen with the new moon is due to earth- 
shine, still does not enter the lists in its defence. 

One strange and haunting figure there was who caught up the 
new doctrine with the impassioned ardour of an apostle, who 
bore it through Europe like a torch, and until its flames were to 
turn and light the faggots of his own pyre. This was Bruno, 
monk of Nola, last of the great martyrs of the Inquisition. He 
must have heard the message early, for even as a young acolyte 
in the cloister, he had turned back his monkish cowl to bear the 
message to his kind. " At the door of the soul of youth sounded 
Coppernicus' imperative word," he writes in after years ; the 
thrill of the youthful impress stirs him still. The reading of 
the book was epochal in his life ; he feels as if he had been 
suddenly freed from chains. The truth which he now may see, 
which he may almost grasp with his hands, had seemed to him 
hitherto hid as with a veil. He seizes upon the new teaching 
as if it responded to something in his innermost soul. By a 
flash of genius his vision ranges beyond that of Coppernicus 

M 



1 78 THE WORLD MACHINE 

himself ; he looks upon the firmament of stars and proclaims 
them suns. Marvellous prevision that another scant half- 
century will confirm! 

Bruno was not an astronomer ; he was a poet and a meta- 
physician, and perforce of these something of a mystic. So 
far as demonstration or proof go he contributed little to the 
establishment of the new theories. Still, in a worldly way his 
influence must have been wide. He became a sort of evangelist 
of the larger light. 

It is evident that in the face of such a philosophy as he had 
evolved, the oriental fictions which then served the world for 
faith could hardly keep their hold. At barely twenty he is 
summoned under accusations of heresy. There must have been 
a deal of it abroad, for friendly tapers fit him by night from 
monastery to monastery until, after three years' wandering, 
the borders of Italy are reached and he is free. He tarries for 
a little at Geneva ; but it is only twenty-six years since the 
hand of Calvin had given over the philosopher Servetus to be 
burned. He goes to Toulouse, famous for its university ; then 
to Paris. There he becomes a high favourite of the astrology- 
loving Henri III. A special chair is created for him at the 
university, because as a heretic he may not say the mass ; his 
eloquence attracts great audiences. A little later he goes to 
England in the suite of the French ambassador. He must have 
been fascinating in conversation ; Elizabeth was among those 
who felt his charm. He is incidentally a maker of plays ; 
Shakespeare, impartially appropriating everything in sight, as 
was his wont, revamps several of them as his own. 

Bruno's stay in England was the happiest, as it was the most 
fruitful, of his wandering life. He is holding public disputations 
at Oxford, going about among the homes of the titled and the 
enlightened. London was then hardly larger than, let us say, 
Brighton or Omaha. Here he may readily have met Bacon, 
Shakespeare, Ben Jonson. It may have been his influence which 
made Gilbert a Coppernican. Bruno was then near thirty- 
five, and in the plenitude of his powers. It was there that he 
perfected his philosophy, developed his ideas. It was there 
that he turned from academic Latin to express his ideas in a 
language understanded of the people. With Montaigne he is 
the first of the moderns to deal with philosophical and scientific 
questions in the common speech of the people, as did the 



BRUNO 179 

ancients. He chose for the most part the form of the Platonic 
dialogue. He handles it lightly and easily. A little later, 
when Galileo wins literary renown, he employs the same form. 

It was in England that Bruno wrote the two volumes in 
which he gave the widest expression to his cosmical theories. 
The first of these was La Cena de U Ceneri, the Ash- Wednesday 
Evening's Supper. It owed its title to its peculiar origin. Sir 
Fulke Greville, a friend of Sir Philip Sidney's, had invited a 
company of philosophers to dine and hear his defence of the 
Coppernican ideas. When the book finally appeared, even 
though it was written in Italian, it must have aroused a tempest ; 
he was compelled for some time to remain in concealment. Yet 
this was in the England of the Golden Age of Elizabeth. 

But Bruno was not content merely to announce the new 
truth ; he stood forth to do battle. He must have been a 
disturbing guest ; wherever he goes he sows unrest ; he is a 
warrior against his time. When he returns to Paris with his 
patron and friend, the French ambassador, he offers the rector 
of the Sorbonne a modest tract of one hundred and twenty 
theses — it is the habit of the time — in which he sets forth his 
philosophy and his variance from the accepted belief with a 
boldness and precision which must have made that distinguished 
functionary gasp. Strange to say, the document was printed 
and publicly read. Perhaps they were preoccupied with other 
things ; Paris was then in civil tumult ; he takes his way across 
the Rhine. At Marburg he is denied a hearing ; but at Witten- 
berg he meets with a remarkable reception. The stately little 
mediaeval town passed then for the Athens of Germany ; he 
spent here two happy years, writing, lecturing, defending his 
faith. 

The civil power changes ; he dwells for a time in Prague, 
in Helmstatt, finally in Frankfurt-am-Main, finding his living 
as a corrector of proofs, publishing his own books, and living, 
since he is denied right of residence in the city itself, in 
a near-by monastery. There he receives an invitation from a 
rich young man, son of a noble family, to come to Venice. It 
is his end. Whether or not he was deliberately trapped is not 
clear ; at any rate he is shortly after denounced to the Inquisi- 
tion by this wretched miscreant. In Venice he might weU have 
thought himself safe ; but even there the power of the Inquisition 
was strong. 



i8o THE WORLD MACHINE 

He is human ; he offers to recant and forswear. It is not 
enough. For six long years he languishes in prison. There, 
from the visions of the stake the terror falls ; his soul grows 
great and strong. When he stands at last in Rome before his 
judges to receive their decree, he answers it with splendid 
courage : " It is you that tremble at your sentence more than 
I." In the customary formula, he is handed over to the civil 
authorities, "to be dealt with as mercifully as possible and 
without the shedding of blood." Lest there should be any 
confusion, it should be noted that the civil government of Rome 
was still in the hands of the Church : the governor was a 
monseigneur. 

They burn him in the Campo di Fiori, the flower-market ; 
the day is a fete for the populace. A ghastly crowd of prelates 
hovers round to see him die. The Pope from the distant palace by 
St. Peter's watches the curling smoke. But his agony brings 
not one shriek ; his tongue was bound lest in the end he should 
blaspheme. In the flower-market to-day stands the slender, 
hooded figure of this knight-errant of the truth, looking with 
mournful and relentless eyes over across the river towards this 
same palace of the popes. They could give his slight and 
quivering frame to the flames ; but the message had gone forth. 
The hand of the monster has been struck with a palsy ; it will 
burn no Brunos now. 

Bruno was truly a martyr to the new world system. He 
taught a plurality of worlds, and it was this, and not the 
Coppernican ideas of the motion of the earth, which was 
absolutely irreconcilable with the teachings of the Church. The 
inhabitants of distant planets could hardly all be derived from 
Adam ; it could hardly be for them that the Son of God had 
been crucified. The purely Coppernican ideas of the earth's 
motion, though they involved essentially the conception of the 
grandeur of the sun, the comparative insignificance of the earth, 
might still be entertained perhaps without utter discredit to 
the Hebraic teaching. In the whirling cosmos sketched by 
Bruno, the idea of a Fall and Redemption became simply 
grotesque. It must have been this that aroused the churchly 
guardians ; they were not yet awake to the danger that 
threatened them. It is not until sixteen years after the murder 
of Bruno that the work of Coppernicus was put upon the Index. 

It is tragic to reflect that Bruno's frightful fate seemed to 



BRUNO i8i 

have all the effect that its authors could have desired. His 
books were forgotten ; Galileo hardly ventures to mention his 
name. He seems to have found no disciple. 

In the face of the grandeur of his ideas, and his unquestioned 
powers of exposition, this seems strange. The truth is that 
Bruno was in advance of his time ; more than that, the parts of 
his system most original to him, and which to-day make us 
marvel at the previsions of his genius, were unsusceptible of 
proof. It is simply amazing now to go back and consider how 
far beyond the ideas of Coppernicus the marvellous deductions 
inspired by his powerful and fervid imagination had swept him. 
Among moderns he is the first to reach again the heights of 
vision of Democritus and proclaim the infinity of worlds. The 
spaces of the heavens, he taught, are peopled with other systems 
resembling our own. The stars are suns ; round them circle 
other planets, or, as he more vividly put it, other earths, doubt- 
less like unto ours. The only reason that we cannot see these 
other systems is due simply to the unthinkable distance at 
which they lie and to the littleness of their planets. Seen from 
a similar distance, our earth would be equally invisible, our sun 
but a twinkling star. 

He divines much more. From Nicholas of Cusa he had 
learned to see flecks upon the sun, whose veritable existence 
Galileo was afterwards to prove. From these he imagined the 
turning of the sun. With increasing astonishment do we read 
that not merely does the sun revolve upon its own axis, but 
it has a movement of translation as well ; and, again, that there 
are probably other planets belonging to our own system which 
cannot be seen because of their distance. It took one hundred 
and sixty years of study with the telescope to verify the latter 
fact, while the truth of the former has only been demonstrated 
in our own day. 

So far does his vision reach beyond that of his master that 
we may agree with Riehl in believing that he was the first to 
conceive the true construction of cosmos. He was a sort of 
somnambulist of the infinite. More than any other man for 
two thousand years he had put off the fetters of space and 
time. He pictured the infinitude of worlds as peopled with an 
infinitude of created forms, perhaps similar to those upon our 
earth, perhaps higher than these. Only a fool could believe 
that in unending space the unlimited creative might of the cosmos 



1 82 THE WORLD MACHINE 

would result in the formation of but a single inhabited world, 
lighted by a single sun. Life in all its stages was a universal 
fact. He seems even to have caught some dim glimpse of the 
idea of evolution. As a philosopher he must explain the exist- 
ence of evil ; what we call evil he believes is, in truth, but the 
limitation of our view. In an infinite universe all things must 
and do exist in order that it may have completeness. He whose 
eyes may see but parts of the whole cannot see the glancing 
beauty and the glory of the All. In the larger universal life 
he found the compensation of the ills that burden the slender 
part we know. 

Bruno was the godfather of Spinoza ; of pantheism, too. 
His was the first scientific religion invented by man ; probably 
it is still the only rational religion which advancing knowledge 
will permit us to retain. What is certain is that this earth 
has seen few more heroic figures. His ideas, like his trust, 
were sublime. Much that he taught could have been with him 
but conjecture. Yet in so far as we have advanced in knowledge 
his ideas have been confirmed, point by point. We know to-day 
that the stars are suns, that dark planets exist in systems 
beyond our own, and that the material of the universe is the 
same. 

It is pathetic, if it be not the essence of tragedy, to reflect 
that this John the Baptist of the new evangel might have been 
forgotten from the memory of men were it not for the chance 
discovery which came eight or nine years after his soul had 
passed in flame. It is pathetic, if it be not the essence of 
tragedy, to reflect that his heroism accomplished nothing. The 
aged Galileo, forswearing the truth upon his knees, took the 
part of civil wisdom. The invention of a fumbling apprentice 
was to be worth more to the advancement of the race than 
the martyrdom of the greatest intellect then walking amid the 
ways of earth. 



CHAPTER XV 

KEPLER: PIONEER OF THE MODERN IDEAS 
OF NATURAL LAW 



" And who were they," I mused, " that wrought 
Through pathless wilds, with labour long, 

The highways of our daily thought ? 

Who reared those towers of earliest song 

That lift us from the throng to peace 
Remote in sunny silences ? " 

Lowell, Masaccio. 



CHAPTER XV 

KEPLER: PIONEER OF THE MODERN IDEAS 
OF NATURAL LAW 

There is much in history to make it seem as if genius were 
a thing born to triumph spite of every difficulty. Village 
Hampdens, mute Miltons there may be, in uncounted number ; 
but the history of the men who have made history leaves a doubt. 
The thing seems innate ; circumstances appear to have little 
to do with its development. This is more or less Darwin's 
view, and Darwin, we know, was counted in his youth not so 
very bright, and so intended for the clergy. Buried, it would 
seem, tenfold deep in his canonry at Frauenberg, and spite of 
his priestly tasks, Coppernicus could still evolve the system 
that dethroned the earth from its position as the centre of the 
world. Isaac Newton's mother would have made him a farm- 
boy, but he neglected his work ; it was no use trying. From a 
like obscurity came the strange figure which bore onward the 
flame kindled by Coppernicus, and lighted the way for Newton's 
triumphs. 

Along in the waning years of the sixteenth century, at about 
the same time that Shakespeare was holding horses before the 
doors of the London theatres and Francis Bacon was a struggling 
young barrister, there was a pot-boy in the little province of 
Wurtemberg, serving the peasants round about, their beer. He 
was a sickly lad, prone to violent iUnesses. Perhaps it was on 
this account that he was sent to a monastic school near by. 
Perhaps he found favour with the monks who taught him. 
Anyhow, he found his way to the University of Tubingen. 
There he fell under the influence of Michael Moestlin, sectarian 
of the new gospel. Even in this out-of-the-way corner the 
leaven was at work. It had set a ferment in the brain of 
Michael Moestlin. He passed it on to this sickly, eager lad 

who bore the name of Johann Kepler. This young Kepler's 

185 



1 86 THE WORLD MACHINE 

first bit of writing was on the double motion of the earth. Soon 
he got a professorship at the little University of Gratz. 

All the time his teeming head was busy with a problem that 
had got into it and would not out. This was as to the cause 
of the motion of the planets, and why there are just six. He 
makes what he thinks is a great discovery — a purely fanciful 
one, however — that the number is due to the fact that there 
are just five regular solids, and this obviously corresponds to 
the gaps between the six planets ! His idea is in thorough 
keeping with the time ; it is a survival of the old Pythagorean 
mysticism of numbers. He writes a book about it, which con- 
tains, for the rest, some curious speculations about a force 
emanating from the sun which may be responsible for planetary 
motion. 

The little volume wins for him the friendship of Galileo, 
then a rising young professor at the old University of Padua. 
It likewise brings him into communication with Tycho Brahe, 
a Danish nobleman turned astronomer, and greatest scientific 
figure of the age. Kepler is a convinced Coppernican. Tycho 
is not, and will not be so long as he lives ; instead, he devises 
a system of his own. Full of his theories, Kepler goes to see 
him, and they discuss a great difficulty. 

Coppernicus had swept away the clumsy system of epicycles 
handed down from Ptolemaic days. He made the planets move 
in circles ; but it was plain as a pikestaff that they did not. 
Tycho was one of the greatest observing astronomers that ever 
lived — the Herschel of his time. His observations made it all 
too clear that the planets would not always appear where the 
simple theory of circles supposed them to be. 

If there be any one who would know how great discoveries 
are made, let him listen to the dictum of Newton : "I intended 
my mind." Upon this problem Kepler intended his mind for 
eight long years. He tried every device under the sun; none 
of them would work. One day he thought to see if the planetary 
motions would fit into an ellipse ; he sought after* these things 
with that almost insane intensity that some men seek gold ; 
his joy at finding that he had hit the truth at last was almost a 
delirium. 

Even before this his meditations and endless, ceaseless cal- 
culating had disclosed one great law. This was that a line 
joining any planet and the sun — the radius vector, as the 



KEPLER 187 

geometers say — sweeps out in its revolution equal areas in equal 
times. This fitted perfectly with his second discovery, that the 
orbit of the planets was an ellipse. He could now announce the 
first two of what have ever since been known as Kepler's Laws. 
This was in 1609, the same year, by chance, that news of a 
curious optical contrivance in Holland was brought to the ears 
of Galileo. 

Does the idea lurk anywhere that these world-explorers, 
reaching, through their studies, to larger and larger views of 
the cosmic adventure, work on in a cold and bloodless equani- 
mity, unimpassioned, unmoved ? The stuff that explorers are 
made of is not this. Perhaps the ultimate spirit of scientific 
endeavour may best be personified in an image of truth carved 
of impeccant marble ; the temper of her devotees who have 
laid at her feet her richest garlands is far otherwise. Discoverers 
are seers, poets — poets in the largest and highest sense. In the 
flush of divination the hand of Newton trembles, the pen of 
Kepler sings. When the long nights of vigil, the days of toil, 
are ended, when success has come, he breaks into rhapsody, in 
the strain of the Hebrew prophets of old. 

When he had at last worked out the formula which goes by 
the name of his third law, he was nearing fifty. The volume 
in which it was announced opens with a burst of poetic splendour 
as naive as it is rare — lines that leap and words that thrill : — 

" What I prophesied two-and- twenty years ago, as soon as 
I discovered the five solids among the heavenly orbits — what I 
firmly believed long before I had seen Ptolemy's Harmonies — 
what I had promised my friends in the title of this book,^ which 
I named before I was sure of my discovery — what sixteen years 
ago I urged as a thing to be sought — that for which I joined 
Tycho Brahe, for which I settled in Prague, for which I have 
devoted the best part of my life to astronomical contemplations, 
at length I have brought to light, and recognised its truth 
beyond my most sanguine expectations. It is not eighteen 
months since I got the first glimpse of light, three months since 
the dawn, very few days since the unveiled sun, most admirable 
to gaze upon, burst upon me. Nothing holds me ; I wiU in- 
dulge my sacred fury ; I wiU triumph over mankind by the 
honest confession that I have stolen the golden vases of the 
Egyptians to build up a tabernacle for my God far away from 
1 Harmonices Mundi (1619), Introduction. 



i88 THE WORLD MACHINE 

the confines of Egypt. If you forgive me, I rejoice ; if you are 
angry, I can bear it ; the die is cast, the book is written, to 
be read either now or by posterity, I care not which ; it may 
well wait a century for a reader, as God has waited six thousand 
years for an observer ! " 

The third law, announced in this exulting paean, came nine 
years after the other two. It embodied his discovery of the 
simple relationship which subsists between the distance of the 
planets from the sun and the time of the planetary year — that 
is, that the cube of the distance is proportional to the square 
of the time of revolution. Stated in other terms, the speed of 
each planet in its orbit is inversely as the square root of its 
distance from the sun. The product of the distance into the 
square of the speed is the same for each planet ; the ratio of 

— ^ for every planet is the same. 

Simplicity, predictability, mechanical fixity, the whole 
scheme under the governance of law, in lieu of mystery or caprice 
or the whims of the gods ! This is what the discoveries of 
Kepler meant. They were among the earliest of the attempts 
to reveal a single common principle at work throughout broad 
groups of phenomena, among the first of those " laws of nature " 
which measure the degree of progress attained in any branch of 
natural inquiry. Archimedes, it is true, had established the 
laws of equilibrium in a time long gone. Galileo was even 
then at work on the " laws " of motion. But Kepler's were 
the first of the great generalisations which, like mighty monu- 
ments, mark the advance of the human mind. He was a 
pioneer. His fame is just. 

He had triumphed ; he had established for all time a truth 
— the greatest work, says Taine, open to man. But he did not, 
could not, see the further meaning of the laws he had unveiled. 
He could not divine the cause, the mechanical necessity, which 
lay beneath his laws of planetary motion ; before that could 
come a new science must be developed ; it was even then being 
developed, and, stranger than all, by his friend and correspondent 
in the University at Padua. 

Still, it is amazing to find how near he came to divining it 
all. We have seen that some idea of planetary attraction 
floated vaguely before the mind of Coppernicus. With Kepler 



KEPLER 189 

it took on a very definite form. The work which appeared in 
1609, in which he announces the first two of his laws, con- 
tains an introduction which came perilously near to a complete 
anticipation of the ideas of Newton. 

Every natural substance,^ he says, by nature remains in 
repose when it is isolated and outside the sphere of activity 
of bodies which have an affinity for it. He anticipates Galileo. 
Gravitation, he goes on, is an affection or quality with which 
bodies are endowed in order to hold them together. This 
faculty or property is general ; but the globe of the earth does 
not attract a stone any more than the stone attracts the earth. 
Bodies are not drawn towards the earth's centre because it is 
the centre of the world, but as the centre of things of the same 
species and of the same family. If the earth were not round, 
bodies would not be drawn towards its central point, but would 
tend in different directions. If the earth and the moon were 
not held in their orbits by some force, the earth would mount 
towards the moon by the fifty-fifth part of their distance, and 
the moon would descend the remainder of the distance in 
order to be united to it. The sphere of the moon's activity 
extends as far as the earth and attracts the waters of the torrid 
zone. The moon passes to the zenith ; the waters follow it 
and mount with it, more notably in the deep and open oceans, 
with less liberty in the Mediterranean and in gulfs. 

If this action of the moon extends to the earth, it follows 
equally that the force of the earth's attraction extends to the 
moon. No portion of matter which exists on the earth can 
lift itself up and escape from its powerful grasp. There is 
nothing intrinsically light or weightless. All bodies are material ; 
lightness is only a less degree of weight. Even the moon cannot 
slip its leash. 

Surprising in the last degree it is to meet with these perfectly 
just ideas in a work appearing a generation before Newton was 
born. But Kepler does not stop here ; he has shown that the 
planets which have the swiftest movement are those nearest 
the sun ; the farther they are from the sun, the slower their 
motion. What is their motor force ? It can reside only in 
the planets and the sun itself. These two recognised effects, 
diminution of the speed with the increase of distance, must have 
one and the same cause. But the centre of the world where 

1 Quoted from Bailly, Histoire de V Astronomie Moderne (1779), ii. 41. 



190 THE WORLD MACHINE 

this motive force resides can be only the sun which, as the 
regulating power of the universe, determines the distance and 
the speed of each planet. Just as the moon moves round the 
earth in virtue of the earth's attraction, so are all the planets 
held in chains and kept in their orbits by the preponderant 
force of the sun. You read and you gasp a little to find how 
close he presses the quarry. 

Still, these general ideas are not sufficient ; he is a mathe- 
matician as well as one of the earliest of modern physicists. 
He has studied deeply the phenomena of light. He has found 
that mathematical law determines distance and speed. Is it 
possible that a mathematical law can express the force of this 
attraction ? He has observed that light grows feebler the 
greater the distance from the source of illumination. Con- 
ceivably the motor force from the sun is weakened in the same 
way. You perceive wherein he erred. 

If there be such a force acting outwards from the sun, it is 
evident that it must extend in all directions — that is, in the three 
dimensions of space. It is not a question here simply of the 
contour of a circle, but of the surface of a sphere, and since 
spherical surfaces are to each other as the squares of their radii, 
it follows that light grows feebler in proportion to the square 
of the distance. It is astonishing, but this obvious fact escaped 
Kepler and his time — yet another illustration of the truth that 
the human mind does not march ; it creeps. Bound up to 
the erroneous idea of a simple proportion, Kepler concludes that 
the attractive force of the sun is the same. Only a step separated 
him from the law of inverse squares. 

He seeks even to identify this attractive force. Gilbert of 
Colchester's great work, The New Physiology of the Magnet 
(how quaint the title to our ears !), had appeared in 1600. 
Kepler had read it with profound attention. Gilbert had com- 
pared the earth to a huge magnet ; he surmised even that this 
might be the attractive force of the planets ; he had said that 
the earth and moon act towards each other like a pair of magnets. 
Kepler takes one step further ; he likens the sun to a vast and 
still more powerful magnet, and this magnetic force for him 
was the secret of the sun's attraction. He even meets the 
objection that if such a force existed, it would be cut off during 
an eclipse. He points out that just as magnetism may act 
through other solid bodies, it may act through the planets 



KEPLER 191 

themselves. It may be true, he says, that during an eclipse 
there is some change, some alteration in this force, and hence 
in the direction of the planetary motion. This may, he con- 
jectures, explain why the orbit of the planets is not a perfect 
circle. He just misses the splendid intuition of Newton that 
this attractive force being reciprocal, when one body circles 
about another it pulls this other out from the centre, so that 
its own path becomes an ellipse. 

His fancy knows no rein : thus will he endeavour to ex- 
plain why it is that the earth and other planets do not fall into 
the sun. Some force must hold them in their course. Kepler 
is a poet ; he is dowered with one of the most vivid of imagina- 
tions, quite as wonderful, we may believe, as that of any Milton 
or even Shakespeare. For him the universe is alive ; the earth 
is a great animal — the tides are its breath. He considers the 
spheres, the stars, as inhabitants of the ether. In the ether they 
are born, in the ether they live like plants and animals ; they 
are the butterflies of space. They maintain their motion by 
virtue of an animal force which resides within them. 

His exuberant imagination leads him astray. He has per- 
ceived clearly enough the first part of the first law of motion, 
that bodies at rest tend to remain at rest so long as they are not 
acted upon by any exterior force. He does not perceive that 
the planets need no urging force, that once set going and un- 
impeded, they will go on for ever. It is not given to any one 
human mind to grasp the truth whole. Newton could not. 
What wonder if Kepler failed ? The minds even of the greatest 
of each generation are bound up, limited, in some sense per- 
verted, by the preconceptions born with them. When the 
tireless, teeming brain of Kepler was searching, searching, 
searching for causes, reasons, effects, no science of mechanics 
existed. It is this alone, we may conceive, which withheld 
from him the glory of having demonstrated what he had divined, 
from having reduced all planetary motion to a single principle, 
from having revealed the whole solar system as the workings 
of a vast machine. 

No matter, it is enough ; the paths of the planets are now 
absolutely known, proved. The Coppernican idea has received 
a perfectionment that amounts almost to a demonstration. 
Hardly any longer will it be possible for any timid Peter to 
deny the truth. One step more and it will no longer be possible. 



192 THE WORLD MACHINE 

Still, it is the old story. He is a generation ahead of his 
time. His ideas must wait. It does not seem as if his publica- 
tions made any considerable impress. They were, in truth, so 
written as to repel more sober minds. Amid his wild flights 
and mystical fancies, the great truths they contained were 
almost lost. His Epitome of the Coppernican Theory is a 
sane and admirable work, long used as a textbook. His Optics 
was one of Newton's earliest treasures. The Inquisition does him 
the honour to put his books on the Index, but this is simply 
because the Church is then engaged in suppressing the whole 
Coppernican heresy, which has been stirred to a dangerous 
flame by the discoveries of Galileo. The Grand Duke of Tuscany 
sends him a golden chain ; but this was probably at Galileo's 
instigation. 

But not one mind among all his contemporaries, not even 
Galileo's, sees the importance of his discoveries. Galileo, perhaps 
from a deeper weakness, quite ignores them. Descartes will be 
busy in a few years constructing the universe out of the simple 
ingredients of matter and motion. He is devising a mechanism, 
and he has need of every scrap of help he can get, for as yet 
the facts are scant ; but he does not appear ever to have read 
a line of Kepler's works. The Novum Organum appears eleven 
years after the New Astronomy, in which Kepler gives the 
first two of his immortal laws, — two years after the Harmonies 
of the World, in which the third and final law is announced ; 
but for the whole Coppernican scheme Bacon has only a sneer, 
for Kepler no word. 

Almost the whole of Kepler's life was passed in bitter poverty. 
Now he is getting old, his salary is long in arrears, the pinch 
grows tighter ; his child had died of smaUpox, his wife of a 
slow fever, and he had scarce money enough to pay for their 
burial. 

At last, exhausted by a journey to Prague to plead for the 
payment of his due, his slender meed of strength depleted by 
days and nights of tireless research, disheartened by failure, worn 
out by the vicissitudes of an existence for the most part wretched 
enough, he too takes a fever and dies at fifty-nine. He had 
struggled up from a pot-boy in a country tavern, struggled 
through lifelong ill- health, through difficulty and misfortune. 
But he did not live to enjoy his fame. The Golden Fleece for 
which he sought, time laid upon his bier in after years. 



KEPLER 193 

It is a sorry story, not of persecution, not of torture, but 
of that long agony of martyrdom that Hes in utter neglect. 
The times had strangely altered when the nations, through 
their representatives, might gather to do homage to a Pasteur. 
They had indeed changed greatly in the succeeding fifty years. 
But meanwhile yet another brilliant investigator, leading a far 
different life, had likewise to drink the cup of bitterness for his 
services to the truth. The far north had produced Coppernicus. 
Germany had added Kepler. Let us journey southward, and 
along the quiet ways of sunny Tuscany, list to the story of 
Galileo and his starry woes. 



CHAPTER XVI 
GALILEO AND THE OPTIC TUBE 



THE JUDGMENT AGAINST GALILEO 

To assert that the sun, immobile and without local movement, 
occupies the centre of the world is an absurd proposition, false in 
philosophy, and moreover, heretical, since it is contrary to the 
testimony of the Scriptures. It is equally absurd and false in 
philosophy to say that the earth is not immobile in the centre of 
the world, and this proposition, considered theologically, is at least 
an error of faith. 

Congregation of the Index, 1633. 



THE ABJURATION 

" I, Galileo Galilei, son of the late Vincenzo Galilei, of Florence, 
aged seventy years, being brought personally to judgment, and 
kneeling before you Most Eminent and Most Reverend Lords, 
Cardinals, General Inquisitors of the universal Christian republic 
against heretical depravity, having before my eyes the Holy 
Gospels, which I touch with my own hands, swear that I have 
always believed, and now believe, and with the help of God will in 
future believe, every article which the Holy Catholic and Apostolic 
Church of Rome holds, teaches, and preaches. But because I have 
been enjoined by this Holy Office altogether to abandon the false 
opinion which maintains that the sun is the centre and immovable, 
and forbidden to hold, defend, or teach the said false doctrine in 
any manner . . . with a sincere heart and unfeigned faith, I abjure, 
curse, and detest the said errors and heresies, and generally every 
other error and sect contrary to Holy Church ; and I swear that 
I will never more in future say or assert anything verbally, or in 
writing, which may give rise to a similar suspicion of me ; but if I 
shall know any heretic, or any suspected of heresy, that I will de- 
nounce him to this Holy Office, or to the Inquisitor or Ordinary of 
the place where I may be. . . . At Rome, in the convent of Minerva, 
22nd June 1633, I, Galileo Galilei, have abjured as above with my 
own hand." 



CHAPTER XVI 

GALILEO AND THE OPTIC TUBE 

Ye who listen with creduhty to the teaching of authority, and 
pursue with eagerness the fictions of hfe, who beHeve that human 
goodness may survive the temptations of power, or that the 
virtues of a reUgion are exemphfied in the deeds of its adherents, 
attend to the melancholy history of a prince of the human mind. 

A few years after the birth of Francis Bacon, a few months 
before that of Shakespeare, and on the day that Michael Angelo 
was closing his long and stormy career in Rome, the wife of 
Vincenzo de Galilei, descendant of a noble Florentine family, 
brought into the world the child who came to be known by 
his forename of Galileo. The father was poor ; he was a 
musician, something of a mathematician too ; he even wrote a 
book defending the freedom of scientific inquiry. He was poor, 
and he had no mind that his son should follow the same hard 
path as he. He thought to make of the boy a cloth-dealer ; 
it was no use. In school he showed the most precocious talent, 
out of school he was for ever inventing mechanical toys. This 
was not the stuff for a shopkeeper ; so, at a hard sacrifice, the 
boy is given a chance to attend the university in his native 
town of Pisa. The Medici in their glory had endeavoured to 
make it a rival of the schools of Bologna and Padua ; they had 
done well by it. There was none better anjrwhere. 

The boy is now destined to be a physician. He shall at 
least follow the most lucrative of the sciences, if his bent be 
that way. His mathematical father knows to his cost how 
little mathematics are prized; the chair in the University of 
Pisa receives the magnificent salary of sevenpence-halfpenny 
a day. Old Vincenzo will save his son from that ; but fate 
is strong. 

The family is a good Catholic one, so is the boy ; but his 
mind is restless. On his knees one day in the cathedral, his 
wandering eye watches the swing of a great lamp which the 



198 THE WORLD MACHINE 

verger had just lighted and thereby set in motion. In that 
day there is a dearth of clocks, and the young student of medicine 
wants a machine that he may count pulses by. He observes 
that the time of the lamp's swing remains, so far as he can 
decide, the same, though its path of motion grows less and 
less. He reflects upon his observation, tests the matter when 
he has a chance ; the isochronism of the pendulum is discovered 
anew. Not that the pendulum had not been known before. 
We may trace it back to the Arabs. It was even known in 
Europe a century before Galileo's time. But discoveries made 
headway slowly then ; it had not come into general use. Galileo 
gave it a practical turn, made of it a pulsilogy, a pulse-counter. 

His mechanical instincts were now wide awake. One day, 
soon after, he overhears a lesson in Euclid. It is good-bye to 
medicine. A few years later, at twenty-six, all the apprehensions 
of his practical father are realised ; Galileo is appointed pro- 
fessor of mathematics, with the princely income of sixty scudi 
a year, something like ;f 13. No matter ; destiny, in Emersonian 
phrase, is working through him and in him ; already he has 
made a discovery great enough to bear his fame through all 
the coming years. 

One day a treatise of Archimedes falls into his hands ; he 
gets to thinking over the laws of falling bodies. For the first 
time in history, so far as we know, he measures the rate of the 
fall. His earlier discovery with the pendulum here stands him 
in good stead, and he lays the foundations of a new science, 
the science of bodies in motion, what we call to-day dynamics. 

He is young, ardent ; this restless, inquiring habit of mind 
gets him into difficulties. One of the foolish, unverified dogmas 
that had come down from Aristotle is that heavy bodies fall 
faster than light ones — that a twenty-pound weight will fall 
twice as fast as a ten-pound weight. There are plenty of 
people in the world who believe this still. Galileo questions 
it, stirs up a hot controversy about it, and to prove his ideas 
he mounts Pisa's celebrated Leaning Tower, and lets fall a 
hundred-pound and a one-pound shot. The whole university 
is there to watch the weights fall ; there is no question that 
they strike the ground together. Any one who has eyes to 
see may see. But the philosophers of the books will not believe. 
They simply intensify their dislike of the young man who had 
shown them they were wrong. In a little while he gets an offer 



GALILEO AND THE OPTIC TUBE 199 

of another post, and is very glad to go. It is a hard day for 
the university. His glory might have been its glory ; but he 
never returns. 

At his new post at Padua he perfects the new mechanics, 
and meditates upon the great work which, other interests having 
been sated, he will dictate and give to the world in his blind 
and helpless old age. All the while he is growing to a profound 
interest in astronomy. He studies his Coppernicus long and 
thoughtfully, opens his correspondence with Kepler, and, as we 
have seen, writes to Kepler in his first letter that he has long 
been a convert to the new ideas. There is a paragraph in this 
letter which reveals well his state of mind, and very vividly 
the state of the times. He says : — 

" I have collected many arguments for the purpose of refuting 
the accepted hypothesis ; but I do not venture to bring them 
to the light of publicity for fear of sharing the fate of our 
master, Coppernicus, who, although he has earned immortal 
fame with some, yet with very many (so great is the number of 
fools) has become an object of ridicule and scorn. I should 
certainly venture to publish my speculations if there were more 
people like you. But this not being the case, I refrain from such 
an undertaking." 

" So great is the number of fools ! " Remember that from 
near by Venice very soon after, a champion of these same views is 
taken to Rome in chains to be roasted over a slow fire. By-and- 
by, when his fame is spread wide, Galileo will have more courage ; 
but for his courage there is scarce a schoolboy who does not 
know how dearly he will pay. He will wait, but in the interval 
he is polishing that mordant wit, perfecting that strength of 
exposition, which is to make him one of the masters of modern 
Italian prose. 

In the year 1604 such little part of the world as thinks upon 
such things is disturbed. A new star swims into its ken. In 
the bible of Aristotle there is no accounting for this. Still, 
the star is there. Galileo lectures about it. They must have 
been wonderful lectures, for such a throng gathers that the 
university theatre is inadequate ; he speaks in the open air. 
The philosophers of the books are again irritated. A great 
controversy springs up, and now it is that, with all the polished 
weapons of the subtlest dialectics, with a wit and gorgeousness 
of illustration and clear and convincing argument that make 



200 THE WORLD MACHINE 

him a deadly antagonist, he stands boldly forth as the defender 
of the Coppernican system. 

It is given to no man to construct the orbit of his time. 
The outcome of the controversy we know ; but those who 
listened to his flashing satire, his impassioned defence, could 
hardly have guessed. Probably there were open-minded, im- 
partial men in that day who heard and were still unconvinced. 
Not the sanest and the wisest among them, not even Galileo 
himself, could have dreamed that in neighbouring HoUand a 
meddlesome apprentice was possibly even then stumbling upon 
a curious device which was to be a stone in a sling for the 
slaying of one of the most Goliathan of myths that ever stalked 
the camps of human thought. 

It is curious to think now how long men had before them 
the elements of this toy which in the hands of Galileo was almost 
to shake the earth from its foundations. When spectacles were 
invented we do not know. The burning-glass must have been 
thousands of years old ; of Archimedes* achievements with the 
burning-mirror old Plutarch has left us an entertaining legend. 
The explorer Layard found among the ruins of the palace of 
Nimrud, at Nineveh, a convex lens of rock-crystal, which makes 
it clear that even in that far-off day something of the powers 
of this especial shape of rock-crystal must have been known. 
Ptolemy of Alexandria wrote a treatise on refraction. Roger 
Bacon in the thirteenth century described a telescope, though 
he probably never made one. Still, the wondrous result of 
putting a pair of lenses one before the other remained un- 
disclosed. 

Be that as it may, we know that along in the fourteenth 
century, perhaps before, spectacles came into use. Then, as the 
story runs, a Dutch apprentice mounted a pair of lenses on a 
stand, and looking through them, it was noted that the neigh- 
bouring church steeple appeared to be drawn very near, and 
to be turned upside down. This was the initial discovery. It 
seems clear that some sort of telescope, more likely just a kind 
of field-glass, came speedily to be made and sold in Holland. 
It is on this ground that Galileo's title to the discoverer of the 
telescope is disputed. But no one seems to have thought for 
a moment of pointing one of these affairs at the stars. That at 
least was all Galileo's own. 

In some fashion a vague report of these odd little affairs 



GALILEO AND THE OPTIC TUBE 201 

came to Galileo's ears. Mark that he was then long past the 
age at which great inventions are usually made. He was then 
forty-six. But his youthful enthusiasm, energy, resourcefulness, 
were not gone. He travelled back to Padua from Venice, 
where he had heard the story, and sat up all night thinking 
about it. He had mastered all the physical knowledge of his 
time. Kepler had written a book about optics, which he had 
doubtless read. By morning his invention was complete. A 
piece of old pipe served him for a tube, a pair of spectacles 
glasses for lenses. His device was not that of the Dutchman 
at all, and though it would only magnify three diameters, it 
did not invert the image. He took his invention back to Venice, 
and all the senators and distinguished men of the place had a 
look. It made a big sensation, and Galileo enjoyed it to the 
full. Immediately they doubled his salary, and made him a 
professor for life. Then he set to work grinding bigger and 
better lenses. Soon he had a telescope, the first real telescope 
ever made, one that was capable of magnifying thirty-two 
diameters ; and with that he was off in the starry ways, reach- 
ing into depths of space no man had ever reached before, and 
bringing back such marvels that the world was in amaze. 

This is in the year 1609, the same year that Kepler, all 
in ignorance of the impending discovery, had completed and 
sent forth his New Astronomy or Celestial Physics. It is just 
sixty-six years since Coppernicus' book had come from the press. 
How the patient old Polish canon would have stared if only 
he might have had a look along with the Venetian senators ! 
Could he perchance have written then so calmly, with such 
even pulses, of the things he would have seen ? Galileo could 
not. He is in a fever of excitement. Time will not run half 
slowly enough to make all the discoveries he sees within his 
grasp ; and he is making them, coining them, as Americans 
would say. He starts what is near to a newspaper to publish 
them to the world. 

Reflect that this telescope of thirty-two diameters is the 
best he ever had — no better than a good ship's glass now. But 
what a flood of light it sheds ! Almost at the very first the 
moons of Jupiter are disclosed, four of them, turning round 
about the larger planet. This, too, is not in the books. It is 
disturbing, upsetting. Had not Aristotle taught that the 
number of the planets is seven, and could Aristotle lie ? But 



202 THE WORLD MACHINE 

Galileo had also looked upon the face of the moon, found it 
full of mountains and valleys and volcanoes, and not at all the 
smooth, bare, and crystal surface that Aristotle, again, had 
taught. He had explained the appearance of " the old moon 
in the new moon's arms " as due to earthshine ; he made the 
earth a planet shining like the rest. He turned upon the Milky 
Way, and showed that its nebulous haze was in reality a crowd 
of stars, so thickly sown and individually so faint as to give 
the appearance of a gossamer cloud. Then he saw that Saturn 
appeared to consist of three parts ; he had the first sight of 
the famous rings. The old Aristotelian world was crumbling 
in his hands. 

Then came the final blow. It followed from Coppernicus* 
theory that Venus and Mercury, could we see them closely 
enough, would show phases like the moon, though Coppernicus 
himself did not make such a prediction, as is so often said in 
the books. Galileo with his glass saw Venus grow from a 
crescent to its full splendour and then back again. His dis- 
covery of the satellites of Jupiter had shown that other planets 
might have moons revolving round about them, just as has 
the earth. The phases of Venus was almost the last stone 
required in the Coppernican structure. Kepler is overjoyed ; 
he longs for a telescope with which to see it all himself. 

But for the last and final proof Galileo searches long and in 
vain. When he turns his telescope to the stars he is astonished 
to find that they appear to grow no larger. Their distance from 
the sun must be unthinkably immense. What is more, when 
he tries to discover if any among them change their apparent 
position as they should, seen from one side of the earth's orbit 
and from the other — that is to say, in the spring and in the 
fall — ^he can detect no motion. He cannot even find any parallax 
for the sun. The answer that Aristarchus made to objectors 
to his theory must remain the answer of Galileo and the Cop- 
pernicans of that day ; but it is hard to believe. Try a moment 
to grasp it all now. In the sky is a body so vast that it has 
an appreciable visual diameter — a huge disk, in fact — and yet 
it is so distant that from two distant points on the earth it 
will show no parallactic shift of position, even with a telescope, 
at least any such a telescope as Galileo could contrive. Yet 
vast as is its distance from the earth, the stars themselves are 
so remote that even this immeasurable distance becomes a point. 



GALILEO AND THE OPTIC TUBE 203 

Sometimes in our haste we condemn men like Bacon because 
they could not see the new truth, despite all the proofs that 
Galileo brought to bear. We judge Bacon for his vain boasting, 
not for his ignorance, or lack of comprehension ; for is it so 
clear that if it could all be brought to us afresh, untrained to 
an unreasoned acceptance of such ideas from the thoughtless 
days of childhood, we should find them so easy and convincing, 
even now ? We may venture not. The world has little changed. 

Still, the arguments brought against the new doctrines were 
for the most part sorry stuff. There is one preserved to a luck- 
less fate which illustrates the mush and muddle which even 
then could pass for argument. No sketch of the period could 
well be without it ; we may have it here. It is an extract from 
the pen of Francesco Sizzi, a Florentine astronomer, who exposes 
the absurdity of Galileo's discoveries thus : — 

" There are seven windows in the head, two nostrils, two 
eyes, two ears, and a mouth ; so in the heavens are there two 
favourable stars, two unpropitious, two luminaries, and Mercury 
alone undecided and indifferent. From which and many other 
similar phenomena of nature, such as the seven metals, &c., 
which it were tedious to enumerate, we gather that the number 
of planets is necessarily seven. 

" Moreover, the satellites are invisible to the naked eye, and 
therefore can have no influence on the earth, and therefore 
would be useless, and therefore do not exist. 

" Besides, the Jews and other ancient nations, as well as 
modern Europeans, have adopted the division of the week into 
seven days, and have named them from the seven planets : 
now if we increase the number of planets the whole system 
falls to the ground." 

Crumbling, falling, is this old system, to carry down in its 
fall all that is bound up with it ; but it has time, strength, to 
deal out through the arm of its upholders one last shameful 
blow. 

The establishment of the phases of Venus gave to the Cop- 
pernican system that plausible air of reality which comes from 
successful prediction, from the verification of any truth which 
follows as a necessary consequence of a theoretical view. When 
by deduction from a broadly generalised system of facts we may 
reach out into the unknown to foretell that which is as yet 



204 THE WORLD MACHINE 

obscure or even undivined, the human mind finds a comforting 
sense that it is upon soHd ground. 

The knowledge of the system of sateUites which circle about 
Jupiter offered yet stronger support. This little world about 
the great planet, says Humboldt, " presented to the intellectual 
contemplation of men a perfect image of the larger planetary 
and solar systems." It was soon recognised that these satel- 
lites, or planets of a secondary order, obeyed the laws discovered 
by Kepler. The squares of the times of their revolution were 
as the cubes of the mean distances of the satellites from the 
primary planet. The mere discovery of the existence of these 
sateUites threw the whole old-time conceptions into confusion. 
The establishment of the fact that they followed the general 
laws of planetary motion brought in anew the element of pre- 
dictability, of consequence, and completed the rout. 

These were among the services which Galileo and his glazed 
tube rendered to the intellectual advance of the world. There 
was yet another which seemed to still more profoundly influence 
the mind of the time. This was Galileo's discovery of the sun- 
spots, and through these the sun's rotation. The human kind 
had not yet left off all relics of the primitive sun-worship. The 
disclosure which the telescope had brought that the face of 
the moon was crossed and scarred with mountains and valleys, 
had sorely troubled the Aristotelian dogma of the perfection of 
the planets ; the spots upon the face of the sun was the finishing 
stroke. 

The triumph of the telescope and its creator was now 
complete. Kepler could write proudly to his friend : Vicisti, 
Galileo ! He had won. The Florentine court had brought him 
back in honour to his native Tuscany. There was no more 
celebrated man now in all the earth. Perhaps he gloated a 
little in his strength. The rapier of his wit made enemies ; 
they gathered for his undoing. The Church began to awaken 
to its peril. The Mosaic cosmogony was being sundered and 
riven by the hands of its friends. It is to be remembered that 
Galileo, nominally, at least, was, like Coppernicus, a good 
Catholic ; and so he remained to the end. 

In Florence was a zealous priest whose enmity he had 
incurred. Soon came mutterings from Rome. Thither Galileo 
was called. Never did his powers of dialectic shine more. He 
writes back that he is winning all along the line ; but he reckons 



GALILEO AND THE OPTIC TUBE 205 

ill. The forces of obscurantism were too strong. Kepler had 
written an admirable exposition of the Coppernican idea, backed 
up with all the new knowledge and the new proof. To Galileo's 
dismay, this and the work of Coppernicus himself are now put 
upon the baleful Index of the Forbidden and their circulation 
interdicted to Catholic lands. Galileo himself returns home 
under formal orders never again to teach or believe in the 
motion of the earth. He could plead never so eloquently the 
new cause. Kepler might write from beyond the Alps : — 

*' Eighty years have elapsed during which the doctrines of 
Coppernicus regarding the movement of the earth and the im- 
mobility of the sun have been promulgated without hindrance, 
because it is deemed allowable to dispute concerning natural 
things, and to elucidate the works of God ; and now that new 
testimony is discovered in proof of the truth of these doctrines 
— testimony which was not known to the spiritual judges — ye 
would prohibit the promulgation of the true system of the 
structure of the universe ! " 

It was of no avail. The might of the Church bent to crush 
this formidable new heresy. 

This was in 1616, the year that Shakespeare ceased upon 
the Avon. A time goes by. There is a new Pope ; he is 
Galileo's friend. Things will go better now. Galileo goes again 
to Rome, and has many talks with his friend. The Pope writes 
back to the grand- duke in warm terms of approbation. Galileo 
returns, and sets to work upon his most noteworthy literary 
achievement. Dialogues on the Ptolemaic and Coppernican 
Systems. By 1632 it is done, through the press, and being 
read with an avidity which never greeted scientific work before. 
It is a wonderful piece of literary skill, not in Latin, but in 
rich and nervous Tuscan, full of keen-edged irony and flash- 
ing like a sword. It is one of the treasures of Italian prose. 
It brings a storm. 

There is no need to tell again the oft-told shame. Galileo 
is again summoned. Honours and age — he is now nearing 
seventy — will not save him ; he had disobeyed. Apologists 
of the Church have attempted to mitigate the infamy that 
followed by refutation of the belief that he was ever put upon 
the rack. It is possible he never was. How far his courage 
held, we do not know. He may have been taken to the torture 
chamber ; the threat may have been enough. When Bruno 



2o6 THE WORLD MACHINE 

went to the stake Galileo was thirty-six, and not two hundred 
miles away. When he went the second time to Rome, it had 
been but eight years since Archbishop Antonio de Dominis, 
philosopher and man of science, known to us as the explainer 
of the rainbow, had been sentenced to the same fate : *' to be 
handed over to the secular arm to be dealt with as mercifully 
as possible without the shedding of blood " — so the hideous 
formula ran — a sentence that was carried out upon his lifeless 
body and writings after his death in the dungeons where he 
had languished six years. It had been but three years when, 
at Toulouse, these same vicars of Christ had cut the tongue 
from the living Vanini and given his body to the flames. 

Ah, yes ! he recanted ; the miserable abjuration was signed. 
The greatest mind in Europe went home a prisoner. Friendly 
offices saved him from the papal dungeons. He was kept im- 
prisoned in his own house. The degradation, the ordeal, perhaps 
the torture, broke his splendid spirit. He had been a sufferer 
almost all his life from a racking malady ; his beloved daughter 
died ; then darkness came. *' Alas," he writes sadly, in one of 
his letters, ** your dear friend and servant is totally blind. 
Henceforth this heaven, this universe, which by wonderful ob- 
servations I had enlarged a hundred and a thousand times 
beyond the conceptions of former days, is shrunk for me into 
the narrow space which I myself fill in it. So it pleases God, 
so therefore shall it please me." 

Still he labours on. His disciples were allowed to gather 
round him — Torricelli, Castelli, Viviani ; their devotion helped 
to lighten the heavy burden of his years. He is allowed an 
amanuensis, and then it is that he gathers together the fruits 
of his long studies in mechanics, and dictates the most enduring 
of his works, the Dialogues on Two New Sciences. It appears 
in 1638. He is then seventy-four years old. 

But the relentless vengeance of his persecutors never ceased ; 
they tried to stop the publication of his last great work. They 
did delay it for some years. He was allowed visitors rarely. 
One of them was young John Milton, doing his wanderjdhre. 
His visit to the wonderful blind old man must have impressed 
him profoundly. It must have come back to him strangely 
when he too, in the living darkness of his old age, sat down 
to dictate Us masterpiece. You see it reflected in some of 
the finest passages of Paradise Lost. 



GALILEO AND THE OPTIC TUBE 207 

But the talons of the Inquisition could not hold their prisoner 
long. At seventy-eight he passed beyond their reach. He 
passed in poverty, in blindness and disgrace — the greatest 
intellectual glory of Florence and modern Italy. At Arcetri, 
a little hamlet in the hills back of the Tuscan capital, they 
show you the wretched hovel where he died, a prisoner of the 
bloodhounds of the Church. 

It was his discovery and enlargement of the powers of the 
telescope, and the things that he saw thereby — doubtless also 
the tragic ending of his brilliant life — that gave to Galileo his 
wide renown. But by far the most important of all his varied 
contributions to the intellectual wealth of his kind was his 
treatise founding the science of mechanics. While Kepler was 
establishing the laws which govern the motion of the planets, 
Galileo was penetrating the laws which govern the motion of 
bodies on the earth. 

Now, here is a singular thing — not singular, perhaps, if looked 
at aright, for it is a familiarly recurring fact throughout all the 
intellectual development of the race, but puzzling none the less. 
Kepler in Germany, as we have seen, was haunted with his 
endeavours to explain the cause of planetary motion ; he had 
likened the sun, as we have seen, to a vast magnet, and tries 
to find out if its force weakens directly with the distance or 
with the square of the distance. He can find no facts, no 
data, which will give him a clue. Yet Galileo had mined out 
the material for him and put it in a little Latin treatise on 
mechanics, written in 1592. Their friendship began early, and 
ended only with Kepler's death. They exchanged many letters, 
exchanged ideas, exchanged books. 

But Kepler, so quick to grasp the ideas of Coppernicus and 
carry them still further, so proud of Galileo's discoveries in 
the heavens, hailing them with delight even when they over- 
turn some of his most cherished notions, yet cannot link with 
his own thought, nor see the bearing of Galileo's measures of 
motion and his mechanical laws. These would have given him 
just the material he sought ; could he have grasped the import 
of his friend's far more important discoveries in mechanics, he 
would have completely anticipated Newton, as he came so 
wonderfully near to doing. But no, he cannot see. 

You marvel, but it is the same with Galileo. What, so far 
as we know, no other man who had ever lived had thought of 



2o8 THE WORLD MACHINE 

doing, he had done ; he had conceived gravity as a measurable 
force, and himself made the measure. He had established the 
rate at which bodies fall, shown that it was independent of 
the slope or angle of the descent, shown that any projectile, 
rifle-bullet or cannon-ball even, follows this same law and falls 
to the ground by virtue of this same force. He had even gone 
further and divined the last needful element of a complete 
theory ; he had seen with Kepler that not only does a body 
at rest remain at rest if acted upon by no extrinsic force, but, 
further than Kepler, that a body in motion remains in motion 
unless there is some force to stop it. 

The puzzle of the ancients with regard to the movement 
of the planets — and it was Kepler's puzzle too — was the force 
that kept them going. Galileo showed that once in motion no 
further force was needful. Unless something got in their way, 
they would simply keep on going. It was but a step from the 
earth to the skies, from the movements of terrestrial bodies 
to those of the heavens ; but ah ! what a step ! Kepler had all 
but built a bridge ; Galileo had in his hands the keystone that 
would complete it. Like Kepler, he had read the work of 
Gilbert. But he, too, could not see the import of the thought 
and work of his friend, even as Kepler could not see that of his. 

Galileo was deeply interested in the tides ; the true theory 
of the tides had been worked out by Poseidonius and others, 
far back in the Greek days. Galileo prided himself as a scholar ; 
he had studied Archimedes with larger results than any man 
before or since. He must have known well the writings of the 
ancients. Kepler, mixing therewith some of his too exuberant 
fancy, still had a tolerably correct idea. Galileo went all wrong, 
and going wrong just missed, as Kepler missed, robbing Newton 
of his fame. He fumbled the movement of the earth and the 
movement of the oceans. Could he but have caught the true 
theory, instantly his combining, measuring, experimental mind 
would have seen that if the moon can draw the tides, the earth 
may draw the moon. He would have seen in a flash the con- 
nection between the fall of bodies, the path of a cannon-ball 
and the path of the moon. 

He would have caught up his pen and calculated the rate of 
the moon's descent towards the earth each moment, fifty or eighty 
years before a raw lad had come up from Lincolnshire to Cam- 
bridge to study mathematics because he was no use on a farm. 



GALILEO AND THE OPTIC TUBE 209 

His failure brings no reproach ; it cannot dim his glory. 
He did a work which, in sheer variety and quantity as well as 
decisive effect upon the thoughts of men, has never been sur- 
passed, and has been equalled but once or twice in the history 
of the race. His industry was incredible. It is said that many 
of his manuscripts were burned or lost. The complete edition 
of his extant works fills seventeen solid volumes. That day 
had no stenographers nor typing machines ; sixteen hundred 
of his letters upon scientific subjects have been preserved. He 
made his own telescopes, ground and polished his lenses with his 
own hands. He was one of the inventors of the thermometer. 
If he did not invent the microscope, at least he perfected it 
and made it practical. In Florence they have a museum 
wherein they proudly preserve the endless variety of instru- 
ments which he devised and made. 

As an inventive genius you may put him beside Archimedes, 
as an experimental investigator beside Faraday. He was a wit, 
a poet, and a musician, a critic of art and letters and a great 
stylist as well. He had such a myriad mind as Democritus, 
Eratosthenes, Leonardo, Thomas Young. Persecution, im- 
prisonment, poverty, a blind and pitiful old age, accentuated 
it may be by the fright, if not the actual fact, of torture at the 
rack, were his reward. The Powers of the Dark could crush 
him in his helpless age ; but not the fruits of his splendid mind. 
He died miserably, but his work survives. In some sense, the 
conception of a world machine is his creation. 

With a deeper meaning than when Kepler penned the line, 
the years have written for his epitaph : — 

ViciSTi, Galileo ! 



CHAPTER XVII 

THE ADVANCE TOWARD A RATIONAL 
WORLD CONCEPTION 



For these dogmas are long since exploded which asserted that 
all parts of the firmament are wheeled round in perfect circles, 
with excentric and epicycles to preserve their circular motion. The 
absurdity of which notions have thrown men upon the extravagant 
ideas of the diurnal motion of the earth, an opinion which we can 
demonstrate to be most false. And it is " likewise evident that 
although the opinion of Coppernicus about the earth's rotation can- 
not be confuted by astronomical principles because it agrees with 
phenomena, yet it may easily be exploded by natural philosophy. 

Bacon, Advancement of Learning, 



It is not the aim of nature, we must needs believe, that all men 
should see the truth ; but that the truth shall be seen by some, and 
that by tradition it shall be conserved. 

Renan, Dialogues Philosophiques. 



CHAPTER XVII 

THE ADVANCE TOWARD A RATIONAL WORLD 
CONCEPTION 

At the close of the sixteenth century and in the beginning of 
the next, a revolution was accomplished in the thoughts and 
ways of men. It was effected by the disclosure of new facts, 
by the invention of new instruments, mechanical devices which 
widened and extended the primitive faculties with which man 
is endowed. The fore-figures in this revolution were the men 
who devised the instruments, who dug out the facts — men who 
made permanent additions to the stock of human knowledge. 

If we were to believe literary history, the case is far other- 
wise. It is for this reason, and for this alone, that any word 
were needed of an extraordinary figure who claimed, and who 
has received from the literary students of the scientific advance, 
a pretentious place. That is Lord Bacon. There is a chapter 
of interest which might be written, in a larger history of in- 
tellectual development, on the worth of philosophers — pure 
philosophers, as opposed to the school of investigation and 
experiment. If one were to put together a list of their mistakes, 
one might be led easily to the captious conclusion that their 
worth has been of the least. 

Than Lord Bacon there has been no more notable example. 
Few men have ever received more fulsome eulogy ; few have 
ever deserved it less. The work of Bacon has been appraised 
by many a hand ; the appraisal has ranged from something 
akin to deification to that of unmeasured denunciation. The 
literary estimate of the author of the Great Instauration is 
exemplified, and it perhaps reached its apogee, in the famous 
essay of Macaulay. There are few who do not recall his glow- 
ing lines : — 

" It is by the Essays that Bacon is best known to the multi- 
tude. The Novum Organum and the De Augmentis are much 
talked of but little read. They have produced a vast effect 



214 THE WORLD MACHINE 

upon the opinions of mankind ; but they have produced it 
through the operation of intermediate agents. 

"No book ever made so great a revolution in the mode of 
thinking, overthrew so many prejudices, introduced so many 
new opinions. . . . Cowley, who was among the most ardent, 
and not among the least discerning followers of the new philo- 
sophy, has, in one of his finest poems, compared Bacon to 
Moses standing on Mount Pisgah. It is to Bacon, we think, 
as he appears in the first book of the Novum Organum, that the 
comparison applies with peculiar felicity. There we see the great 
Lawgiver looking round from his lonely elevation on an infinite 
expanse ; behind him a wilderness of dreary sands and bitter 
waters, in which successive generations have sojourned, always 
moving, yet never advancing, reaping no harvest and building 
no abiding city ; before him a goodly land, a land of promise, 
a land flowing with milk and honey. While the multitude 
below saw only the fiat, sterile desert in which they had so 
long wandered, bounded on every side by a near horizon, or 
diversified only by some deceitful mirage, he was gazing from a 
far higher stand on a far lovelier country, following with his 
eye the long course of fertilising rivers, through ample pastures, 
and under the bridges of great capitals, measuring the distances 
of marts and havens, ^and portioning out all those wealthy 
regions from Dan to Beersheba."^ 

The picture is enchanting, but from it the opinions of men 
of science differ widely. The obverse of the shield you may 
find in the candid pages of Liebig and in many another. "If," 
said Sir David Brewster, " Bacon had never lived, those who 
study nature would have found in the writings and in the 
work of Galileo not only the principles of his vaunted Inductive 
Philosophy, but likewise their practical application to the 
highest efforts of invention and discovery." His real place is 
uncompromisingly laid down in a savage page of Draper : — 

" Bacon never produced any great practical result himself ; 
no great physicist ever made any use of his method. He has had 
the same to do with the development of modern science that 
the inventor of the orrery had to do with the discovery of the 
mechanism of the world. Of all the important physical dis- 
coveries, there is not one which shows that its author made it 
by the Baconian instrument. 

1 Collected Essays : Francis Bacon. 



A RATIONAL WORLD CONCEPTION 215 

" Few scientific pretenders have made more mistakes than 
Lord Bacon. He rejected the Coppernican system, and spoke 
insolently of its great author ; he undertook to criticise adversely 
Gilbert's treatise, De Magnete ; he was occupied in the con- 
demnation of any investigation of final causes, while Harvey 
was deducing the circulation of the blood from Aquapendente's 
discovery of the valves in the veins ; he was doubtful whether 
instruments were of any advantage, while Galileo was investigat- 
ing the heavens with the telescope. Ignorant himself of every 
branch of mathematics, he presumed that they were useless in 
science but a few years before Newton achieved by their aid 
his immortal discoveries. 

** It is time that the sacred name of philosophy should be 
severed from its long connection with that of one who was a 
pretender in science, a time-serving politician, an insidious 
lawyer, a corrupt judge, a treacherous friend, a bad man." ^ 

It might be urged in Bacon's defence that, in truth, he was 
born too early to take in the full character of the revolution 
going on around him — a revolution whose consequences he did 
grasp with a prophetic insight, and which he sketched in pages 
which are among the enchantments of the English tongue. He 
was forty-eight the year that Kepler issued his New Astro- 
nomy and that Galileo's discoveries with the telescope began. 
He died a year before Harvey's treatise on the circulation came 
from the press, though he knew something of his work. 

But the defence does not stand in the light of the parallel 
career of his contemporary, Gilbert of Colchester. The author 
of the New Physiology of the Magnet was born twenty 
years before the author of The Advancement of Learning, 
yet he could accept the Coppernican doctrine where Bacon 
could not. In the midst of a busy life he could make a multi- 
tude of new observations and lay the foundations of a new 
science, as Bacon never did. 

The pages of The Advancement of Learning and the Novum 
Organum are filled with foolish jeers of Gilbert's work ; of 
Harvey's, too. He could neither make discoveries himself 
nor appreciate those of others. He was as jealous as he was 
ignorant. Compared with the great thinkers of his time, he 
appears, moreover, as a mediocre philosopher whose reasoning 
ofttimes is simply childish. He who looks now through the two 
* History of the Intellectual Development of Europe, vol. ii. 



2i6 THE WORLD MACHINE 

volumes of the Great Instauration finds a work devoid of a 
single contribution to human knowledge of even the remotest 
value. While a half-dozen of his contemporaries were making 
a beginning in a half-dozen new sciences, doing a work which 
the centuries will not undo, Bacon in his study conceives that 
he is the founder of all scientific method. He begins his famous 
Instauration : — 

" Francis of Verulam thought thus, and such is the method 
which he determined within himself, and which he thought it 
concerned the living and posterity to know." 

In tills sounding preface we learn that its author is not 
ignorant that he *' stands alone in an experiment almost too 
hold and astonishing to obtain credit ; yet he thought it not right 
to desert either the cause or himself, but to boldly enter on the 
way and explore the only path which is pervious to the human 
mind." ^ 

The italics are not Bacon's. How this vain and empty- 
handed boaster could have so imposed upon his generation, 
to say nothing of the generations which followed, is one of the 
curiosities of literary history. The truth as to the author of the 
" Baconian philosophy " is that he was simply a philosopher ; 
he dreamed while others worked. He may have been of some 
inspiration to others who followed him, and who were stirred 
by his fervid vaticinations ; he must have seemed to the truly 
scientific spirits of his time a sort of Duke of Argyll. 

It is with far greater justice that claims as the father of 
modern scientific method have been put forward for Ren6 
Descartes. It is so that he is regarded by Huxley ; the authority 
of the opinion is assuredly high. 

Man, observed some reflecting sage, unlike the animals, is 
born to think. If ever there were a man to whom this would 
literally apply, it was Descartes. He came of a distinguished 
family in Touraine ; as a child he was known as le petit 
philosophe ; philosopher he remained to the end of his days. 
He had all the faults of his calling. 

When he came of age, most of the great discoveries which 
blazoned the seventeenth century with such a cachet of distinc- 
tion had been made ; his especial mission in life was to disclose 
the mechanism of the world, and, with a single exception, he 
^ Advancement of Learning, p. 2. 



A RATIONAL WORLD CONCEPTION 217 

seems to have ignored them all. There is evidence that he read 
with avidity all that might be written about himself or his 
opinions, either for him or against. He appears to have read 
little else. He had a contempt for the learning of books ; 
doubtless his disdain was not unfounded. Though he wrote 
many himself, it is recorded that when a company of distin- 
guished savants came to visit him in his retreat at Holland 
and they asked to see his library, he showed them his dissecting- 
room, decorated with dismembered chickens and cats. 

Descartes was, says Huxley, an unwearied dissector ; in 
physiology and in mathematics he did an undoubtedly original 
work. It was on the side that probably interested him most 
that he most signally failed. It is as a philosopher possibly 
that he takes highest rank ; he invented an elaborate system, 
which has inspired almost as many imbecile pages as that of 
Kant. His life, if we may trust his English admirer already 
quoted, *' was the consecration of doubt," yet few men ever 
taught more dogmatically of things which they did not know, 
nor described more vividly things that do not exist. It was a 
remark of a witty compatriot that he established doubt as the 
corner-stone of his philosophy, then calmly ignored it the rest 
of his life. 

After all, his philosophy was but an incident, a means to an 
end. Descartes was a mathematician. It was he who applied 
algebra to geometry, and therefore became the founder of the 
analytic department of that excellent art. It was he who, in 
some sense, made possible the achievements of Newton. It was 
in geometry that Descartes believed that he had found the key 
to the invisible — for that matter, to the universe as well. 

When he was twenty-four, on a campaign in Germany with 
Prince Maurice of Nassau, he had a sort of a dream in which 
the whole future of knowledge seemed to lie before him as 
through an open door. It must have been a remarkable ex- 
perience. He has described it at length in his celebrated 
Discours de la Methode, the work which made his early fame. 
Up to this he had led the easy life of a young man with plenty 
of money, had made extensive researches in the gay society 
of Paris, had travelled much. He speedily found that, for him, 
the most interesting things in this world were inside of his head, 
and he spent the rest of his days in tracking them out. He 
tried Paris for a few years more ; but it would not let him 



2i8 THE WORLD MACHINE 

enough alone. He retired to Holland. He must have thought 
well of the advice of Epicurus — " Veil thy days " ; only one 
or two of his friends knew of his address. 

In Holland he changed his residence twenty-four times in 
not so many years. He never married. He had a daughter, 
like Galileo, at whose death he was deeply moved. Beyond 
that, this world seemed to exist for him only as a subject for 
meditation and analysis. In pages that are models of clear 
and simple exposition — like Galileo, again, he was a writer of 
distinction, one of the founders of the exquisite prose literature 
of France — he has detailed at length his method and his ways. 
It is of interest to know that he never worked but a few hours 
a day, and that in bed ; he did not get up until eleven. His 
life was comparatively brief ; he died at fifty-four, having been 
lured to the court of Queen Christina of Sweden and there con- 
tracting a fever. His real career hardly began before he was 
thirty-three, yet few men ever covered a more extraordinary 
range in their studies. 

You catch a glimpse of his method in his famous aphorism, 
cogito ergo sum. This is the keynote of his metaphysics ; it is 
typical of his whole philosophy. He lays hold of the simplest, 
surest, most obvious fact that he may discover. Certain of his 
foundations, on this he builds. And just cis the geometer, start- 
ing with a few simple lines, puts them together into triangles, 
squares, and other figures, and beginning with the simplest 
propositions, mounts step by step to others the most complex 
and abstruse, so Descartes, beginning with propositions over 
which there could seem no possible doubt, rose to conceptions 
that were certainly grandiose if they were not sublime. Un- 
fortunately, they did not turn out to be true. Never did any 
system-monger lose himself more hopelessly in the baseless 
abstractions of his own thoughts. Descartes sought nothing 
less than a complete system of the universe. His mistake lay 
in believing that he might construct it from a series of axioms 
like a geometer. 

Absorbed in the elaboration of his wondrous fancies, for him 
his contemporaries did not exist. His deepest interest in Galileo 
appears to have been the stories of Galileo's persecution and 
torture. He was not in the least of the martjn: mould ; his 
fright was so great that he straight away left off pubHshing 
his chief work, upon which he had been engaged for years, and 



A RATIONAL WORLD CONCEPTION 219 

in which he had revealed his adherence to the Coppernican 
doctrine. Of Kepler he seems to have known little. His vast 
system of tourbillons or vortices is of interest to-day scarcely 
more than as a philosophical curiosity. It bears just the shade 
of a resemblance to the vortex-ring theory of Helmholtz and 
Lord Kelvin. Some day it may be rejuvenated ; but for its 
own time it was a seduction. With the incoming of the simpler 
ideas of Newton, firm grounded upon experimentally demon- 
strated facts, it was forgotten. 

Nevertheless, and in spite of the ultimate downfall of the 
vast house of cards which he had reared, to Descartes belongs 
a distinction that is unique, and that places him among the 
highest of those who have reflected upon the construction and 
march of the bewildering theatre upon which we are born. 
Not forgetting the chance phrase of Coppemicus nor the brilliant 
conjectures of Kepler, it is fairly certain that Descartes was 
the first concretely to picture this world as a mechanism, the 
first to explain its phenomena upon a mechanical basis, the 
first to analyse the universe into terms of matter and motion. 
This he did, not as pure astronomer, not simply as regards the 
sun and planets ; but through the tides and winds, through 
physiology and all the phenomena of hfe, and down to the last 
flutter of an eyelid. 

Descartes found a militant adversary, the Coppernican system 
a suave but insistent defender, in Pierre Gassendi, the worthy 
abbe of Digne ; he is scarcely remembered now outside the 
musty pages of the history of philosophy. Gassendi bore an 
unmistakably important role not merely in French thought in 
the seventeenth century, but in that of Europe as well. He 
was the first conspicuous defender of the Coppernican ideas in 
France after the fugitive propaganda of Bruno ; he was its 
first expositor at the College de France. It was Gassendi, more- 
over, who dug out and gave new life to the ideas and doctrines 
of Epicurus — that is to say, to the physical and atomic theOTJig^ 
of Democritus. 

The result was a curious alignment. The ideas of Descartes 
and the whole bent of his mind were mechanical ; and the first 
worked-out theory which distinctly presented a mechanical 
world conception was the system of Coppernicus, Descartes 
did not reject the system ; but even in the writings published 



220 THE WORLD MACHINE 

long after his death one sees how Uttle it really gripped his 
imagination. The ideas of Gassendi, far less original, no doubt, 
than those of the author of the Discours, were wholly Democritan 
— that is to say, atomic — a system of materialism rather than 
an endeavour to represent the cosmos as a machine. The dis- 
tinction is worthy of note, since the mechanical doctrine, con- 
trary to popular superstitions, assiduously cultivated by ignorant 
or sophistical minds, in no way involves the conception of a 
material substratum. One may be excellent Coppernican and 
good Berkeleyan, firm materialist and no Newtonian. Yet 
Gassendi, perilling his standing as an orthodox theologian, was 
both materialist and Coppernican. 

A reproach is often brought to the door of Gassendi, as to 
that of Descartes, that the ardour of the evangel was subdued 
by an excess of worldly caution. Such ideas come as a rule 
from minds lacking in historical perspective as well as historical 
information. Consider for a moment the state of the times in 
which these men lived. Gassendi was born in 1592, four years 
before Descartes. He was therefore thirty-two years old when 
the Parliament of Paris sanctioned a decision of the learned 
tribunal of the Sorbonne, forbidding " on pain of death that any 
one should teach or hold any doctrine against the ancient and 
approved authors " — that is to say, any one who should dis- 
pute the doctrines of Aristotle and the Church. Remember 
that at this time the ruler of France was its great Cardinal 
Richelieu, and that this decree was obtained from the Paris 
council by Richelieu himself. Take note that this is but eight 
years before the condemnation of Galileo to imprisonment for 
life ; the ardour of persecution flamed no less violently in the 
north than in the south. 

Moreover, this same enlightened cardinal- minister gained 
from the same tribunal a special decree expressly condemning 
the system of Coppernicus, at near fifteen years after the dis- 
covery of the telescope and all its revelations. The new 
doctrines spread in spite of the official ban ; you might infer, 
perchance, that this decree was but a belated survival of mediae- 
valism and was speedily forgotten. Reflect, then, that as late 
as 1675, when all of intellectual Europe had turned Coppernican, 
the university asked for a renewal of this decree and the Parlia- 
ment of Paris was ready to grant its demands. It desisted only 
before the storm raised by the satire of the good Bishop Boileau. 



A RATIONAL WORLD CONCEPTION 221 

Gassendi had signalled his adhesion to the new doctrines in 
two letters addressed to Galileo in 1625 and again in 1632. 
In 1646, named to the chair of mathematics in the CoUege de 
France, he gave a detailed exposition of the new theories with 
all the arguments that might be urged in their favour. He 
observes that the partisans of these theories are very numerous ; 
but that they " do not dare declare themselves because of the 
sentence of the Congregation pronounced on Galileo by some 
cardinals." Ostensibly he professed adherence to the bizarre 
scheme of Tycho Brahe, since he says it is needful to reject 
absolutely the system of Ptolemy, and because the Bible teaches 
positively the movement of the sun. The farce was so obvious 
that probably no one was deceived, and the excellent abb6 was 
able to keep his chair. For the rest, he was, as Lange remarks, 
one of those happy natures that we pardon more readily than 
others. Intellectually a disciple of Charron the sceptic, he 
was not, like Bruno, a disturber. He was amiable, he was 
gay ; he had an inexhaustible fund of good stories ; it seemed 
absurd to burn such a man or cut his tongue out. By way of 
revenge the practitioners of medicine, against whom much of 
his raillery was directed, accomplished what the Church did 
not. He died of a blood-letting. 

It was the fortune of Gassendi not merely to be one of the 
earliest of the Coppernicans, or, let us say, Galileans, in France, 
but to have made an observation which offered the most dis- 
tinctive piece of proof of the new theory since Galileo's observa- 
tions of the phases of Venus. It followed, of course, from the 
Coppernican scheme that we should observe the periodical 
transit of Mercury across the face of the sun. The Arabian 
Averrhoes thought that he had observed it ; Kepler as well. It 
is now known that the transit cannot be observed by the 
naked eye. 

Kepler had taken pains to calculate the moment of solar 
eclipse, and had announced the passage of Mercury across the 
sun's face for the 7th of November 1631. Gassendi, something 
of an astronomer, made preparations to observe it. That day 
the sun appeared half-hidden by the clouds. He thought he 
could perceive a small black spot, but it seemed too slight to 
be the body of a planet. Happily, however, he observed the 
spot carefully, and was rewarded by finding that its movement 
was much more rapid than that of any sun-spot which had ever 



222 THE WORLD MACHINE 

been observed. When it reached the borders of the sun he 
was able to follow its exit distinctly ; there could be no doubt 
that it was in reality the planet. He had the pleasure of ob- 
serving a phenomenon unknown to antiquity ; he liked a good 
phrase, and in allusion to the ancient quest for the philosopher's 
stone, he said : "I have seen what sages have sought with 
such ardour ; I have found Mercury in the sun." 

It was one more heavy buttress added to the Coppemican 
fabric. In the ancient Ptolemaic system, Mercury had been 
set in revolution round the earth like Venus and the sun ; but 
it was difficult on this theory to understand how Mercury could 
be eclipsed by the sun and march across its face as well. The 
thing was simply inexplicable. 

Gassendi sought likewise the transit of Venus, equally pre- 
dicted by Kepler for a month later. Unluckily for him and 
for other observers, awakened by his discovery of the transit 
of Mercury, the passage of Venus seems to have occurred during 
the night. At any rate the first actual observation was reserved 
for a young Englishman, Robert Horrox, eight years later. 

Gassendi was a voluminous writer; several astronomical works 
were among the number. He had in a high degree the historical 
sense ; he was one of the earliest of the moderns to adopt the 
historical form in the treatment of scientific questions. He 
wrote excellent lives of Coppernicus and of Tycho Brah6, on 
the life and death of Epicurus as well ; it is by the latter work, 
perhaps, that he is best known. His criticisms of Descartes 
were models of polemic, keen, politely ironical, good-natured, 
and substantial none the less. He was the first to point out 
that the principle of doubt expounded by Descartes was but a 
fiction, and that the famous " I think, therefore I am " involves 
a quantity of dogmas no one of which have we any absolute 
proof for whatever. He anticipated the nihilism of Berkeley 
by a century. 

Of interest merely as noting the advancement of the new 
ideas, was the unqualified adhesion to the Coppernican doctrine 
by the English philosopher Hobbes. While Bacon was making 
the ideas of Gilbert, Harvey, and Coppernicus a triangular 
target for his fretful animadversions, the father of English 
materiahsm boldly embraced them aU. It is true that he was 
only thirty-two when the Novum Organum appeared, and that 



A RATIONAL WORLD CONCEPTION 223 

by this time even Bacon appears rather as a belated owl blink- 
ing confusedly in the flooding light. 

None the less, if Hobbes was not a pioneer like Gilbert or 
like Bruno, the weight of his influence on English thought was 
great. He was the first prominent thinker, the first widely 
read writer in England boldly to signal his acceptance of the 
new faith. It is to be noted that he was the lifelong friend 
of Gassendi ; it may have been to his acquaintance with the 
Coppernicising abbe that this was in some part due ; what is 
certain is that Hobbes, forerunner by forty or fifty years of 
Boyle, Hooke, Wren, and Newton, turned English philosophy 
from the vanity of the schools and paved the way for this 
brilliant coterie that, in a few years, was to lift England from 
its barbarian estrangement and isolation from the rest of the 
world and make of this dark land the light of Europe. 

The author of the Leviathan lived to an extreme old 
age ; Gassendi was dead in 1655, five years after his great 
adversary, Descartes. Despite the decrees of Rome and the 
Parliament of Paris, it is clear that for some time before this — 
that is to say, in a little more than a century after the publica- 
tion of the De Revolutionibus, and certainly within a half-century 
of the invention of the telescope, the more enlightened portion 
of mankind had become Coppernican. 

Already the thought of the time was reaching out to con- 
ceptions of infinitude and of a grandeur of the universe before 
which the great globe of the earth seemed to shrink, to shrivel, 
almost to disappear, even as some vast creation of legerdemain, 
obejdng the will of the conjurer, before our astonished eyes 
grows subtly less and less and downwards to a point. 

What was the observation which would make it clear to all 
thinking men ? 



CHAPTER XVIII 
THE TRUE GRANDEUR OF THE SUN 



Astronomy considered in its entirety is the finest monument of 
the human mind, the noblest essay of its intelligence. Seduced by 
the illusions of the senses and of self-pride, for a long time man 
considered himself as the centre of the movement of the stars ; his 
vainglory has been punished by the terrors which its own ideas 
have inspired. At last the efforts of several centuries brushed aside 
the veil which concealed the system of the world. We discover 
ourselves upon a planet, itself almost imperceptible in the vast 
extent of the solar system, which in its turn is only an insensible 
point in the immensity of space. The sublime results to which 
this discovery has led should suffice to console us for our extreme 
littleness, and the rank which it assigns to the earth. Let us 
treasure with sohcitude, let us add to as we may, this store of higher 
knowledge, the most exquisite treasure of thinking beings. 

Laplace, Exposition du Systeme du Monde. 



CHAPTER XVIII 

THE TRUE GRANDEUR OF THE SUN 

While Descartes was busy with his air-castles, fabricating the 
world from dreams, others less ambitious to construct a universe 
de toutes pieces were endeavouring to build up a rational know- 
ledge of that corner in which we live, from a foundation of solid 
fact. Without the aid of the telescope, and merely from patient 
observation by means of the two eyes with which he had been 
endowed by nature, Coppernicus was able correctly to delineate 
the relative positions of the planets and depict the order of 
their revolutions round about the central sun ; something of 
their actual spacing as well. But the ideas which men still 
might form of the true dimensions of the solar system — the 
relative grandeur of the earth to its companion bodies — were of 
the crudest. Even at the death of Galileo there remained one 
great mystery. 

The simplest of considerations required that if the sun's 
distance were not infinite, seen from two widely separated points 
upon the earth it should show an apparent shift of position 
with reference to any intervening body — that is, a parallax. 
Thus, if in the transit of the moon or a planet across the face 
of the sun, to the eye of one observer the edge of the planet 
just touched the edge of the sun, to that of an observer at a 
sufficient distance a slight gap between the two should show. 
And if the angle subtended by this gap could then be measured, 
the true distance of the sun might be known. No such parallax 
or apparent displacement could be found ; Galileo, as we have 
seen, sought it in vain. The crude measures of Aristarchus, 
open, as more accurate observations disclosed, to errors of 
hundreds per cent., was still the best that men could find. 

The restless mind of Kepler busied with the problem. Turn- 
ing it over and over, a simple geometrical construction sufficed 
to show him that if the estimates of Hipparchus, not materially 

changed, as we have seen, by Ptolemy or Coppernicus, were 

227 



228 THE WORLD MACHINE 

in any way correct, the sun must needs show a parallax of at 
least three minutes of an astronomical degree. But the sur- 
prising accuracy attained by his friend and patron, the great 
Tycho, made it clear that no such parallax existed. So did he 
perfect his instruments, that Tycho was able to reduce the 
possible errors of observation to a single minute. As no ap- 
parent displacement even of this slender amount could be 
found, it followed that the distance of the sun must be at least 
three times that computed by the ancients. 

But even the ancients had been able to fix with a fair degree 
of certainty the distance of the moon, and this, on the ancient 
calculations, had already spaced the sun at five million miles 
away, and given it a volume three hundred times greater than 
that of the massy earth. Scant wonder is it that even in Cop- 
pernicus* time these estimates should have been deemed simply 
absurd. 

Now, however, Kepler would set the sun not at four or five, 
not at a lower limit of thirteen million miles ; he would give 
it a diameter, not six or seven, but at the least eighteen or 
twenty times the diameter of the earth ; he would compute 
the dimensions of this glowing ball in the sky, not at three 
hundred, but at seven or eight thousand times our globe. The 
thought was grotesque. It was only by a sort of acrobatic leap 
of the imagination, by an immense and violent somersault of 
the mind, that men could reach belief in such unbelievable 
things. 

Consider that the most enlightened people of that time had 
not left off their credulous trust in astrology ; that such as were 
dabbling in the chemic art were still in search of the philosopher's 
stone and the elixir of life ; consider that throughout all Europe 
the most advanced of nations were still hanging, burning, 
torturing miserable wretches for witches (almost without 
exception, be it observed, from among the outcast poor), 
and it will not be difficult to understand why it was that a 
true conception of the world should have such difficulty in 
battling against the prejudices and superstitions which still 
dominated the great body of mankind. 

But the telescope with its disturbing revelations had effected 
a breach ; bit by bit it widened. In free and heroic little 
Holland, where Descartes had found a refuge, there were men 
of a mind to attack the problem anew. One of these was the 



THE TRUE GRANDEUR OF THE SUN 229 

astronomer Vendelinus. He took up again the theorem of 
Aristarchus, but with the advantage of a weaponed eye, to 
determine anew the exact moment of the dichotomy of the moon. 
He had carefully considered the spots upon the moon, and 
determined those which lie at a median point separating the 
half that was illuminated from the half that was obscure. This 
done, in order to detect the exact moment at which the moon 
reached its quarter, it sufficed to mark the instant at which 
these spots were illuminated. Better instructed than Aristarchus 
or any of his successors could have been, he took into account 
also the possible deviations of angle due to refraction by the 
earth's atmosphere. It will be remembered that at the moment 
the face of the moon was cut in twain, Aristarchus had cal- 
culated the angle subtended by the moon and sun at about 
eighty-seven degrees — that is, within three degrees of a right 
angle ; Vendelinus found that it varied but little more than 
half a degree from a right angle. It followed from his measure- 
ments that the sun must be not twenty times, but more than 
two hundred times the distance of the moon — that is to say, 
not four or five millions, but forty or fifty million miles away. 
The boundaries of the universe, which Galileo had boasted he 
had pushed back hundreds of times from anything hitherto 
imagined by men, were receding farther still. Vendelinus had 
made half the step ; the true distance was soon to be disclosed. 

Between Galileo and Newton the most prominent figure 
among observers of the heavens was Dominico Cassini. He 
was a compatriot of Galileo, and acquired a considerable repu- 
tation through his bold and somewhat fantastic projects for 
the construction of telescopes of enormous size. He was a 
tireless worker ; when he was not sweeping the heavens he 
calculated and wrote. His discoveries were numerous ; among 
others, the rotation of Jupiter and Mars, and four new satellites 
of Saturn. He likewise constructed astronomical tables of great 
value. 

It was at the instance of Cassini, who had come to Paris to 
lake charge of the fine observatory then being erected there, 
that the French king sent out the celebrated expedition to 
Cayenne. One of the results of this expedition was to reveal 
the fact that pendulums beat more slowly at the equator than 
in the latitude of Paris ; by revealing the varying intensity of 
gravitation, it suggested that the earth was not a perfect sphere ; 



230 THE WORLD MACHINE 

it was this that enabled Newton and his successors to calculate 
the figure of the earth. But of still greater importance were 
the observations taken upon the position of Mars simultane- 
ously with like observations of Cassini in Paris. The idea was 
to utilise the transit of Mars instead of the moon for the deter- 
mination of the sun's distance. 

It was the first attempt which had ever been made on such 
broad lines — that is to say, from such widely separated points 
of the earth. It was with a fever of impatience that the French 
Academy awaited the return of its deputies. The observations 
were successfully carried out ; combining their results with his 
own, Cassini was able to fix the parallax of the sun, not at three 
minutes, such as the estimates of the ancients had required ; 
not at one minute, which Kepler had thought probable, but at 
slightly less than one-sixth of a minute. Cassini set it at nine 
and a half seconds. 

This fixed the remoteness of the sun at three hundred and 
sixty times the distance of the moon, or eighty-seven millions of 
earthly miles. This was in 1673 — that is, thirteen years before 
the Principia, fifty years after the Dialogues on the Two Great 
World Systems ; it was in the midst of the reign of the elegant 
and easy-going voluptuary, Louis XV., which, like that of his 
similar in England, the second Charles, proved so favourable to 
the advancement of rational ideas. 

A century and more of minute and repeated observations, 
checked and verified by methods most diverse, has not im- 
peached the substantial accuracy of Cassini's results. It was 
still a little under the reality. But before this prodigious cal- 
culation how men must have stood in amaze ! There was now 
no easy or contemptuous brushing it aside. France was then 
the political, the social, the literary, the scientific centre of 
Europe. The expedition to Cayenne had been sent out by the 
king, under the direction of the Royal Academy. The calcula- 
tions were the work of the Royal Astronomer, the official head 
of scientific investigation in the most enlightened of the nations. 
The results had in some sort a royal sanction ; they had, more- 
over, been carried out with a care and precision hitherto 
unknown ; to contest their value was to set one's face against 
all that stood for truth and knowledge in that day. It was a 
wonderful change ; a short fifty or sixty years since the Holy 
Congregation of the Index, sitting at Rome, had denounced the 



I 



THE TRUE GRANDEUR OF THE SUN 231 

Coppernican theory as heretical and impious, and blasphemy 
against the Most High God. 

Instead of endeavouring to smother the truth, a Catholic 
monarch in a Catholic land could now contribute from the 
revenues of his Catholic subjects to advance it. A century later, 
when a yet more favourable opportunity presented itself to 
determine the sun's parallax, not one government but half-a- 
dozen would contribute. This was during the transit of Venus 
in 1761 and 1769. Halley, the friend of Newton, had pointed 
out the advantage of observations on this planet ; like the 
moon, it crosses the sun's face, but its apparent magnitude is 
too small to cause any serious diminution in the sun's light ; 
the moment it touches, the sun's disk is more sharply defined. 
But the plane of the earth's orbit is somewhat inclined to that 
of Venus, so that we are able to witness the transit of Venus 
only twice in a little more than a century. 

When at last it came again, the interest manifested in the 
event was extraordinary — observing parties were scattered from 
the Cape of Good Hope to Siberia and India ; at the second 
transit, from Hudson's Bay to Madras, from Siberia to Cali- 
fornia, from far northern Norway to the South Sea Isles. The 
results, however, were far from satisfactory. They did not 
greatly improve upon the accuracy attained a hundred years 
before. It is only within the last half-century that, by the 
concurrence of a variety of methods, it has been possible to 
attain a result which no further investigations can materially 
change. 

These methods were grounded upon bases very diverse. 
Even while Cassini was observing the transit of Mars, Roemer 
was deducing the velocity of light. Later on, ingenious con- 
trivances in the laboratory have made it possible to fix this 
velocity with great precision, so that, knowing the time which 
light takes to cross the diameter of the earth's orbit, it is pos- 
sible to deduce the distance of the sun by this means. Two 
others were worked out by Leverrier from the observed varia- 
tions in the earth's orbit — one due to the gravitational influence 
of the moon, the other to that of the near planets. These and 
several others of less value unite with more recent and more 
accurate observations on Venus to fix the solar parallax at 
8''' 8, with a probable error of less than one five-hundredth of 
the distance. 



232 THE WORLD MACHINE 

Some idea of the extraordinary accuracy of modern observa- 
tions may be gained from the curious discovery of an actual 
variation in the latitude of several observatories. This variation 
of latitude is apparently due to a minute change in the position 
of the earth's axis, so that it describes a circuit around its 
mean position in the course of about a year and a quarter, 
though never varying from the mean centre more than thirty 
feet. This, it may be remarked incidentally, is the seventh 
of the known periodical movements of the earth, four having 
been discovered since Coppernicus left Europe vertiginous by 
announcing three. 

The solar parallax now agreed upon fixes the mean solar 
distance at very close to ninety-three millions of miles — that is 
to say, approximately four hundred times the distance of the 
moon. Cassini had computed the distance at but six million 
miles less. His error was not great. But reflect upon the fear- 
ful wrench it brought to all the world conceptions which men 
had treasured from practically the beginning of the intelligent 
consideration of nature. A sun six or seven times the diameter 
of the earth was unbelievable enough ; the measurements of 
Cassini made its diameter more than a hundred times. To our 
eyes the moon and sun appear of exactly the same size ; could 
the sun be brought as near to the earth as the moon, its apparent 
diameter would be more than two hundred degrees ; it would 
seem to us as large as 160,000 moons ; it would fill the entire 
heavens, and there would practically be no night. As the 
amount of heat which the sun may shed upon a planet depends 
upon the square of the distance, it follows that with the sun 
at the distance of the moon, the earth would be 160,000 times 
as hot as now. Nothing living could exist for a second ; it 
would shrivel in a flash, and the earth itself return to the in- 
candescent mass from which it sprang. 

The determination of the sun's true distance first made it 
possible to gain a correct idea as to the size and the dimensions 
of the solar system. Coppernicus was able to fix, with an 
accuracy that is still admirable, the relative distances and some- 
what of the relative sizes of the six planets known to him ; it 
is obvious that he could have but little idea of their absolute 
measures. So long as the sun was assumed to be but twenty 
times the distance of the moon, it followed that, for example, 
Venus, at three-tenths of that distance, or six times the distance 



THE TRUE GRANDEUR OF THE SUN 233 

of the moon, was a body not vastly greater. Jupiter, of course, 
was something of a stumbling-block. At five times the distance 
of the sun, it must be at least a hundred times as far away as 
the moon ; but though it evidently had an appreciable disk, 
it was beyond the measuring powers of the instruments of that 
day and for long after. 

With the sun at four hundred times the distance of the 
moon, Venus must be nearly a hundred times, and at its brightest 
it glows like a little moon ; its disk has an apparent diameter 
of over one minute. It takes only a moment to reckon then 
that it must be a planet as large as the earth. It is obviously 
considerably hotter than the earth ; on the other hand, even 
the greatest telescopes show no clear markings such as we may 
observe upon the moon ; it is possible it may have a very 
dense atmosphere and therefore be inhabitable with beings like 
unto ourselves. 

The fortunate career of Cassini fell amid the charming time 
of the salons, when women of wit drew around them brilliant 
coteries of savants, and when the most erudite and accomplished 
of men did not think it beneath their dignity to clothe knowledge 
and recent discovery in language so simple as not to seem dull 
amid the brilliant conversation of that engaging day. A little 
later Fontenelle, discoverer, with Voltaire, of Newton to France, 
and knowing like Voltaire how to temper the arid phrases 
of science with the elegancies of style, caused a polite little 
rustle in the polite little monde of France by announcing the 
plurality of worlds. His slender volume is charming reading 
still. For proclaiming the same fact Bruno had been burned 
just eighty-six years before. 

A plurality of worlds and our earth in no wise unique — 
this was the new angle from which mankind had now to con- 
sider the problems of human destiny and the worth of human 
effort. The earth was not, in all probability, the sole inhabit- 
able planet even of our system ; it was not unique in size ; 
it was soon clear that it was, in point of fact, utterly insignificant. 
Even Galileo's little tubes could measure Jupiter's disk ; at 
its brightest it is almost as large as that of Venus, and it was 
now clear that the son of Jove was sixteen times as far away, 
even at the nearest point which he comes to the earth. If he 
travelled in the orbit of Hesperus he would be two hundred 



234 THE WORLD MACHINE 

and fifty times as bright ; and as the earth appears from Hesper 
of just the same size as Hesper from the earth, it followed that 
here was a planet a thousand times more vast in bulk than 
either. Saturn at nearly twice the distance was almost as huge. 

Huge as they might be, yet all of them taken together — 
the colossal bulk of Jupiter and Saturn, the earth and all the 
other known planets, and two more yet to be discovered, with 
all their satellites, and five hundred asteroids besides — all of 
them combined would not make a thousandth part of the total 
volume of the sun. It was as if in Vulcan's smithy the gods 
had moulded one giant ball, and the planets were but bits and 
small shot which had sputtered off as the glowing ingot was cast 
and set in space. Little man on a little part of a Httle earth 
— a minor planet, a million of which might be tumbled into the 
shell of the central sun — was growing very small ; his wars, 
the convulsions of a state, were losing consequence. Human 
endeavour, human ambitions, could now scarce possess the 
significance they had when men could regard the earth as the 
central fact of the universe. 

Neither then, nor now, did the new knowledge exercise 
greatly the thoughts or lives of men. Still, then as now there 
were a few who reflected a little. It was the fashion of those 
graceful days to say smart things when one could. " What," 
said Maria Theresa to the philosopher Maupertuis, when she 
had captured him from the armies of Frederick the Great, 
against whom she was then at war — '' what does your philo- 
sophy teach you to think of two princes who squabble over 
little patches of the planet you have measured ? " 

" I have no right," was the sedate response of the hero of 
Dr. Akakia, '* to be more philosophic than kings." 

There can be Httle doubt that the New Revelation of the true 
grandeur of the sun, the utter insignificance of our own planet, 
did more to fix the Coppernican idea in the common mind than 
all the arguments from Aristarchus to Galileo and long after. 
So long as the sun could be thought of as small, or even as not 
greatly larger than the earth, it was thinkable that it revolved 
while the earth stood still. After the measures of Cassini, it 
was unthinkable. No stretch of ignorant fancy could conceive 
of a planet or the earth revolving round a minor satellite or 
the moon, or, in varied parlance, a huge cannon-ball around a 
single buckshot. 



THE TRUE GRANDEUR OF THE SUN 235 

To still greater purpose, it was when the earth and its com- 
panion ** wanderers " could be pictured in such guise ; when the 
sun could be thought of as a body so vast that its monstrous 
bulk would envelop a space near twice that occupied by the 
earth and its circling satellite — that the moon pursues its 
orbital way about the earth within a space of half the shell of 
the sun — it was this that could build up the idea of the sun as 
the dominant fact, the ruling force, the monarch of our world. 
It was this which could bring conceptions of its power, and then 
of a power which holds the planets as dogs within a leash. 

But before this latter conception could take hold, men had 
to gain more definite conceptions of power — that is to say, of 
force. And this could, in its turn, arise only from the develop- 
ment of machines, and out of these, a mechanical science. 

This development was even then in full swing. 



CHAPTER XIX 

THE DEVELOPMENT OF MECHANICS: THE 
FORERUNNERS OF NEWTON 



The theories established in one generation become the starting- 
points of successors. Newton, with all his genius, would not have 
detected the law of gravitation had not Kepler and Galileo preceded 
him ; nor could they have made their discoveries had not Greek 
mathematicians supplied the means. It was by the bold and happy 
identification of celestial with terrestrial physics that the great 
thinkers of the seventeenth century made physical Astronomy an 
exact science, making it a part of Mechanics, explaining its pheno- 
mena by those very Laws of Motion which were proved to regulate 
the phenomena of terrestrial bodies. 

Lewes, Aristotle. 



CHAPTER XIX 

THE DEVELOPMENT OF MECHANICS: THE 
FORERUNNERS OF NEWTON 

Beyond doubt, with all his dreams in the day, the mechanical 
conceptions and ideas of Descartes, his thought of reducing all 
phenomena to the regular and calculable movements of a 
mechanism, exercised a profound influence upon the thought 
of the time. His Principia appeared in 1644 ; its preponderant 
influence outlasted near a century ; physical science has perhaps 
never quite lost its impress. 

The work of Descartes did much ; that of Galileo, with its 
more solid foundations, did more. Galileo's Dialogues on 
Mechanics came in 1638. With the faithful aid of Viviani 
and Torricelli, he added during the last three months of his 
life two supplementary dialogues. The work appeared from 
Leyden ; they would not, of course, let him publish it in Italy. 
Coming from such a man it was read all over Europe with a 
profound interest. 

It is curious to observe how distinct was the work of the 
two men, to note what little use Descartes made of Galileo's 
discoveries. His intellectual egotism carried him so far as to 
put out of his reach materials of the greatest value. It appears 
that of any sort of writing, that which influenced him most 
was Harvey's little tract on the circulation of the blood. It 
had appeared in 1629. It was written wholly in the mechanical 
spirit ; it shows clearly that Galileo and Descartes were alike 
but a part of their time, and that the time had taken on a 
distinctly mechanical bent. 

That bent was intensified, the seventeenth century be- 
came pre-eminently the century of mechanics through the re- 
markable discovery that came the year after Galileo's death. 
This was the elucidation of the theory of the suction-pump, 
and through it the discovery of the weight of air, the develop- 
ment of pneumatics. Our common pump is old enough ; its 

<?39 



240 THE WORLD MACHINE 

invention is commonly attributed to Ctesibius, the forerunner 
of Hero in Alexandria. Probably it was known in a crude 
way thousands of years before that. To explain its action the 
ancients had invented the idea that nature had a horror of a 
vacuum, and that if in any way a vacuum was created, what- 
ever of a material nature lay next would rush in to fill the 
emptiness. It is evident enough from the pages of Lucretius 
that they had a clear idea of the weight of the air ; but, so 
far as we know, it never occurred to them to connect the 
pressure of the air with the action of the pump. The simple 
binding link escaped even Galileo himself — another of the thou- 
sands of instances which might be adduced showing the sharp 
delimitations even of the most piercing and far-seeing minds. 

It is told that some workmen, in constructing a house near 
Florence, had put down a rather long pipe and discovered that 
it would not work. The water would rise in the pump to a 
height of about thirty-two feet and no more. When Galileo 
was asked about it he simply made a jest. He loved a fling at 
the ancients ; and observing that evidently nature had a horror 
of a vacuum only to a height of thirty-two feet, gaily went 
his way. StiU he and his disciples must have discussed the 
subject ; and how keen a joy it must have been to these young 
men to talk the new things over with the man who was creating 
the most of them. 

One of these Galilean disciples was Torricelli. Pondering over 
the matter, Torricelli came to the conclusion that if the air would 
sustain a column of water about thirty-three feet high, it would 
hold up other liquids in proportion to their weights ; as mercury 
is fourteen times as heavy as water, the column of mercury 
that it would sustain would be only one-fourteenth as high. 
Viviani tried it and showed that his friend's expectations were 
correct. The meaning of it all was very clear. Air and the 
mercury, or air and the water simply formed a balance : the 
weight of the air was equal to the weight of the column it 
sustained. 

Torricelli's discovery came in the year that followed his 
master's death. It excited the liveliest interest ; the news of 
it travelled fast. In France it reached the ears of twenty years 
old Blaise Pascal, already revealed as a mathematical genius of 
the highest order. It could have been but a rumour, for he 
repeats the experiments in a great variety of ways ; he makes 



THE DEVELOPMENT OF MECHANICS 241 

it perfectly clear that there is a complete analogy between the 
weight and pressure of water and the weight and pressure of 
air — that their effects are the same. But he goes a step further. 

In the course of his experiments Pascal had noted that the 
pressure of water in a vessel is greater towards the bottom than 
at the top. The idea came to him that the same should be 
true of any considerable body of air. Doubtless he had deeply 
studied optics and the refraction of light ; probably he knew 
of the various attempts that had been made to determine the 
height of the earth's atmosphere. It had been measured by 
the Arabian Al-Hazen in the eleventh century and by Poseidonius 
a thousand years before that. If the analogy between water 
and air is complete, then at the top of a high mountain the 
pressure of the air will be less than at its base — the column 
of mercury will sink. Possibly the slight but curious variation 
from day to day in the height of the mercury column, first 
observed by Torricelli, had already given him a prescience of 
the discovery he was to make. At any rate, he sends Perier 
up to the top of a mountain with a column of mercury to test 
the question. It turns out just as he had foreseen. The baro- 
meter in its present-day sense had been discovered. 

Six years later Otto von Guericke, burgomaster of Magdeburg, 
had invented the air-pump. With it he had shown further 
that a pair of copper hemispheres, when tightly fitted together 
and the air pumped out, could not be separated by teams of 
horses pulling in opposite directions. Nature's " horror of a 
vacuum " was simply the pressure of the air. A new science 
— aerostatics, pneumatics — ^was born. 

It is easy to see what an impulse towards mechanical ideas 
and conceptions all these new discoveries must give. They 
had a curious effect in another way ; they emptied the spaces 
of the inter-planetary ways of air ; they left the heavens, save 
for the planets, comets, meteorites which we may see, a void. 
This was a great step. One of the most puzzling problems in 
celestial physics, as we have seen, was the force which urges 
the planets, the earth as well, in their rapid flight. Galileo, 
by the force of his genius, could rise to a clear and definite con- 
ception of inertia, but he had no thought of applying it to the 
movement of the planets. There was nothing to suggest such 
an appHcation. It was clear enough that bodies shot through 
the air meet with a resistance. If the air extends indefinitely 

Q 



242 THE WORLD MACHINE 

throughout space, as most good folk suppose, then what was 
it which enabled the planets to overcome the resistance which 
they must meet ? Poseidonius and Al-Hazen could make their 
calculations as to the height of the earth's atmosphere : there 
was nothing to prove that they were right. 

A very few experiments with the barometer, its revelation 
of the decrease of air pressure with the vertical height, sufficed 
for a new calculation as to the height the atmosphere might 
extend. This agreed fairly well with the estimates made from 
the appearance of the sun and the stars when they are still 
below the horizon. Men could then rise to a conception that 
was wholly new — that, save for material bodies, space is empty. 

After that a propelling force for the planets was no longer 
needful. Speeding through a vacuum with no resistance to over- 
come, it was clear that once set going they would go on for ever. 

It was the development of these new ideas which made it 
possible for the human mind to conceive of action at a distance, 
that is to say, to conceive of a force which could reach through- 
out all space. It was this which opened the way for Isaac 
Newton, and let his understanding pass to conclusions where 
Kepler, Galileo, and Descartes had failed. 

The human mind was reaching at last to clear and practical 
representations of force — what we to-day call energy. Instead of 
the vague notions of levitation and gravitation which they had 
found in the physics of Aristotle, Kepler and Galileo had sub- 
stituted definite notions of a power acting always towards the 
centre of the earth, a force which could exert a certain puU, 
which acts upon all bodies alike. Guericke had demonstrated 
that Galileo's law as to falling bodies applied equally to all 
bodies regardless of their weight, that a cannon-ball and a 
feather dropped in a vacuum reach the bottom together. For 
mystical notions regarding nature's predilections as to a vacuum, 
they had established a clear conception that the air is a fluid 
which may exert a pressure precisely as does water. With the 
establishment of the practical identity in their actions of air 
and water had come a mechanics of fluids. In a very little 
while Boyle and Mariotte had discovered the law which governs 
the " spring " of air, that is, that air occupies a volume directly 
proportional to the pressure exerted upon it. Galileo's primitive 
thermoscopes were being developed into accurate thermometers ; 
they were making the first crude measures of the energy of heat. 



THE DEVELOPMENT OF MECHANICS 243 

Moreover, and this was of the greatest importance, men were 
developing the measuring habit, the habit of exact observation, 
of comparing one force or power with another, generaUsing 
these observations, and deducing from general laws other effects 
up to then unforeseen or unknown. 

It is easy to understand that very soon there were practical- 
minded men alert to take advantage of all this new knowledge, 
and keen to apply it in a practical way. In the very early 
years of the century, while Galileo was at work upon his ex- 
periments with falling bodies, a rich compatriot, della Porta, was 
throwing out some interesting guesses as to the way advantage 
might be taken of the force of steam. Very soon Rivault had 
imprisoned water within a cannon-ball, and blown the ball to 
pieces simply by heating it. Before Galileo's death a number 
of inventors were at work reviving the old contrivances of 
Hero and Ctesibius for doing work with steam. Somewhere 
about 1628, says Thurston, Lord Somerset, second Earl of 
Worcester, had a rude contrivance for raising water working 
in Vauxhall. A little later he had a still more developed 
machine at Raglan Castle. In 1666 he had taken out the first 
patent for a steam-engine. 

It was about this time that a new mechanical device lent an 
added perfection to astronomical observation, for that matter, 
to the whole art of physical investigation — a perfection which 
neither could have otherwise attained. This was the invention 
of an accurate measure of time — in a word, of clocks. It is 
almost beyond belief that they should have come so late. 
Not, indeed, that clocks of one sort and another were not known 
to the most ancient times. Sun-dials were in use, not perhaps 
in the Garden of Eden, where a reminder of the flight of time 
would have been an annoyance, but certainly in prediluvian 
days. Even the Chaldeans knew how to " weigh " time — in 
a word, had clepsydras or water-clocks. Some very wonder- 
ful examples of the latter were constructed by the Arabians. 
The famous clock sent by Haroun-al-Raschid to Charlemagne 
indicated the hours by the fall of little balls and by the coming 
forth of small horsemen from as many open doors. 

It is to the Arabians, too, that we probably owe the first 
application of the pendulum as a time measurer. This was 
certainly made by the great astronomer Ibn-Junis along at the 
end of the tenth century. He thus anticipated Galileo by some 



244 THE WORLD MACHINE 

six centuries. Even before Ibn-Junis it appears that clocks 
had been constructed to run by the aid of weights and not by 
the fall of water. To Pacificus, Archdeacon of Verona, in the 
early part of the ninth century is attributed the first clock 
moved by wheels and weights. It is clear, from a passage in 
Vitruvius, that even the complicated '' machina hydrauUca," 
an actual astronomical clock, constructed by Ctesibius under 
Ptolemy Euergetes in Alexandria, was worked by toothed 
wheels. 

What Pacificus really appears to have done was to invent 
the escapement, an ingenious device wherein he employed the 
inertia of a balance to retard and regulate the movements of 
the hands of the clock. But the pendulum and the escapement 
were not successfully combined in the construction of an accurate 
clock before the seventeenth century was weU advanced. It is 
probable that Galileo in his old age had constructed a pendu- 
lum clock — he certainly gave a description of it ; and Young ^ 
attributes to Sanctorius the same invention in 1612. Neither 
the one nor the other came into any general use. The practical 
invention remained for a young Dutch investigator, Christian 
Huyghens, living at the Hague. He combined all of Galileo's 
skill for invention and the construction of telescopes with some- 
thing of Kepler's genius for the divination of laws, something too 
of Kepler's mysticism and incorrigible tendency to dream. He 
patented his clock in 1657, when he was twenty-eight years old. 

A Httle later the celebrated Dr. Robert Hooke added the 
device of the escapement, and the observer of the heavens had 
in his possession a new weapon. It was far from perfect, how- 
ever, even then. You gain some idea of its value from the 
fact that in the next century the British Government voted 
the clock-maker, Harrison, a reward of £20,000 for his per- 
fectionment of the chronometer. 

Huyghens' clock gave to the searchers of the heavens a 
means of reducing their observations to the same degree of 
accuracy in point of time as two other devices had given to 
their measures and localisations in space. These were the 
mounting of the telescope upon the index bar of a graduated 
instrument, first accomplished by the French astronomer, 
Morin, in 1634 J ^.nd the rigging of fine threads in the focus 
of the telescope to attain micro-metric divisions of the field 
^ Lectures on Natural Philosophy, 1807. 



THE DEVELOPMENT OF MECHANICS 245 

of view, introduced by Gascoigne and Aiizout not long after. 
It was the combination of these which made possible the un- 
dreamed-of precision attained by Cassini and all his long line 
of successors. 

Huyghens was not merely an inventor of clocks and a grinder 
of beautiful lenses ; he was an astronomer and a thinker. With 
the telescopes of immense length which he constructed, he was 
able to discover the first satellite of Saturn and Ukewise clearly 
to reveal Saturn's rings. The discovery of the latter was Uke- 
wise made before he was thirty, and published by him in an 
elaborate study. He made profound investigations into the 
nature of light ; he was the founder of the undulatory theory. 
He had a wonderfully incisive mind, but an unbridled imagi- 
nation as well. The fantastic Cosmotheoros, wherein he sets 
down his wild speculations as to the inhabitants of other planets 
and a hundred other things, reads like Kepler's Somnium 
Astronomicum. You catch a glimpse of the survival of medieval 
traditions, even to this late day, from his remark when he dis- 
covers Saturn's satellite. It is his idea that the number of 
planets and satellites having now reached twelve, and this 
being the perfect number, no more remained to be discovered. 
He would be puzzled, no doubt, could he return now to learn 
of five hundred more found since his day. 

Beyond doubt Huyghens' most noteworthy work was his 
Oscillatorium Horologium, published in 1673. Therein he de- 
scribes in full the pendulum clock, and with it a number of 
important investigations into the theory of the pendulum and 
the allied problems of the motion of bodies in a curve. It was 
in this treatise that he announced the law of centrifugal force, 
obtaining a numerical measure for the tendency of a body 
moving in a circle to recede from the centre. He worked this 
out quite independently of any considerations of planetary 
motion. It was with him a simple problem in mechanics. 
He seems never to have thought of extending this prin- 
ciple to the motion of the bodies he had studied so successfully 
and so well. He was upon the very edge of the discovery 
of the law of gravitation. He made distinct contributions to 
the developing science of mechanics ; he had an essentially 
mechanical mind, and half his life he had spent in the study 
of planetary motion. But so far was he from realising the 



246 THE WORLD MACHINE 

consequences of his own studies and discoveries that thirteen or 
fifteen years later, when the law of gravitation was announced, 
great mathematician as he was, he pronounced it " absurd." 

But with the clearance of the sky, with the emptj^ing of 
space of any resisting medium to retard a planet's flight, with 
the development of mechanical ideas, mechanical formulae, 
measurements of motion, it is easy to understand how there 
were other and younger men interested in the study of the 
stars, eager to apply the new knowledge towards a solution of 
the great problem. They would take up again the fascinating 
suggestions thrown out by Gilbert of Colchester and by Kepler, 
that there is a force acting outwards from the sun, holding the 
planets in their orbits, and decreasing probably in direct pro- 
portion to the distance from the centre of the system. 

These ideas had by no means been lost from view. That they 
were in a sense current coin is evident enough from a passage 
in the Novum Organum. Though Bacon had ignored Kepler as 
he had ridiculed his own countryman, he borrows the ideas of 
both, to refurbish them as his own : — 

*' Again, if there be any magnetic force which acts by sym- 
pathy between the globe of the earth and heavy bodies, or 
between that of the moon and the waters of the sea (as seems 
most probable from the particular floods and ebbs which occur 
twice in the month), or between the starry sphere and the 
planets, by which they are summoned and raised to their 
apogees, these must all operate at very great distances." ^ 

As early as 1645 — that is, a year after the appearance of 
Descartes* Principia — a French mathematician, Bouillaud, en- 
deavours to refute Kepler's idea that such a force would de- 
crease in simple proportion to the distance, and shows that it 
would be as the square. But he seems to be as far as any from 
connecting up such a force with common gravity. 

Borelli, in Pisa, attempts the problem. He is a disciple of 
Galileo, one of the founders of the famous Accademia del 
Cimento, which is the forerunner of the Royal Society, the 
French Academy of Sciences, and all their like ; the author too 
of the celebrated book in which the principles of mechanics are 
first applied to animal motion. In his theory of the " Medician 
planets," the satellites of Jupiter, not published until 1665 but 
probably written long before, Borelli speculates upon '* a natural 
* Novum Organum (1620). 



THE DEVELOPMENT OF MECHANICS 247 

inclination which the planets have to approach the central body 
round which they revolve, an inclination which is held in equili- 
brium by the force of their forward motion." This is not much 
nearer than Anaxagoras or Simplicius, though he offers an ex- 
periment to clinch his idea. He avoids the use of the word 
attraction, and he does not try to reduce the force of this 
inclination to any mathematical expression. 

Along about 1660 there is a company of gentlemen meeting 
in London to discuss all sorts of physical problems. Their head 
is the Honourable Robert Boyle, one of the founders of pneu- 
matics, the author of the Skeptical Chymist, and often referred 
to as the founder of modern chemistry. Among others are Sir 
Christopher Wren, the architect of St. Paul's, mathematician, 
astronomer, and all-round man of science ; Edmund Halley, 
future Astronomer Royal, then not long up from Cambridge ; 
Robert Hooke, who begins as an assistant of Boyle's, reveals a 
marvellous capacity for experiment, becomes the author of a 
hundred inventions ; one of those restless-minded investigators 
who scatter their fire and begin a hundred researches which 
others will take up and complete. 

This company is the nucleus of the Royal Society ; in 1662 
Charles IL, restored to the throne of the Stuarts, gives it a 
charter, and its great work is begun. In the very first year 
after its founding, it appoints one of its earliest investigating 
commissions to report on the subject of gravitation. Boyle is 
a member of the commission ; already he is so thoroughly 
interpenetrated with mechanical conceptions that he likens the 
world to the wonderful clock in Strasburg — that is to say, like 
Descartes, he conceives it as a machine. 

But what is the force which makes this machine go ? 
Evidently he does not see that it is gravity, about which the 
commission is to report, for the inquiry bears no fruit. But 
Hooke is restlessly fretting over the problem. As early as 1666 
he has a paper before the Royal Society, " On the Inflection 
of a Direct Motion into a Curve by a Supervening Attrac- 
tive Principle." Seven or eight years later he had another 
communication to make which contains this remarkable 
passage : — 

" I shall hereafter," he says, " explain a system of the world 
differing in many particulars from any yet known, but answer- 



248 THE WORLD MACHINE 

ing in all things to the common rules of mechanical motions. 
This depends upon three suppositions : — 

" First, that all celestial bodies whatsoever have an attrac- 
tion or gravitating power towards their own centres, whereby 
they attract not only their own parts and keep them from fly- 
ing from them, as we may observe the Earth to do, but that 
they also do attract all the other celestial bodies that are within 
the sphere of their activity ; and consequently, that not only 
the Sun and Moon have an influence upon the body and motion 
of the Earth, and the Earth upon them, but that Mercury, Mars, 
Jupiter and Saturn also, by their attractive powers, have a 
considerable influence upon its motion, as in the same manner 
the corresponding attractive power of the Earth hath a con- 
siderable influence upon every one of their motions also. 

** The second supposition is this, that all bodies whatsoever 
that are put into direct and simple motion will so continue to 
move forward in a straight line till they are, by some other 
effectual powers, deflected and sent into a motion describing a 
circle, Ellipsis, or some other more compounded curve line. 

" The third supposition is, that these attractive powers are 
so much the more powerful in operating by how much the nearer 
the body wrought upon is to their own centres. Now what these 
several degrees are I have not yet experimentally verified ; but 
it is a notion which, if fully prosecuted as it ought to be, will 
mightily assist astronomers to reduce all the celestial motions 
to a certain rule, which I doubt will never be done without it. 
He that understands the nature of the circular pendulum and 
of circular motion will easily understand the whole of this prin- 
ciple, and will know where to find directions in nature for the 
true stating thereof. 

" This I only hint at present to such as have ability and 
opportunity for prosecuting this inquiry, and are not wanting 
of industry for observing and calculating, wishing heartily such 
may be found, having myself many other things in hand which 
I would first complete, and therefore cannot so well attend it. 
But this I durst promise the undertaker, that he will find all 
the great motions of the world to be influenced by this principle, 
and that the true understanding thereof will be the true per- 
fection of astronomy." 

You perceive how closely they are pressing the quarry. 



THE DEVELOPMENT OF MECHANICS 249 

Wren and Halley as well as Hooke have worked it out that such 
a force exists, and that it acts inversely as the square of the 
distance. But all of them realise that they lack the decisive 
proof. They do not as yet see how this theory can be brought 
into agreement with Kepler's laws, as it must ; they have 
many a debate on the subject. A few years later Hooke shows 
a curious experiment with a pendulum, which he likens to a 
planet going round the sun ; but the thing is to prove that the 
path of the planet will be an ellipse. 

One day, doubtless as a jest. Wren offers Hooke and Halley 
a book worth forty shillings if they bring him the demonstration 
within two months. Hooke declares that he has it, but he 
withholds his proof. Since it is not forthcoming, young Halley 
finally travels down to Cambridge to have a talk with one of 
the members of the Society there, a Dr. Newton, Lucasian 
professor of mathematics, a retiring and secretive man, who 
had already sent many interesting communications to the 
Society, his newly invented telescope as well. 

There Halley finds that the whole subject had been worked 
out nearly twenty years before. Such, at least, is the accepted 
tradition. The story is so extraordinary that it is worth in- 
quiring a little as to whether the tradition will altogether hold. 



CHAPTER XX 

NEWTON AND THE MOTOR FORCE OF 
THE WORLD MACHINE 



Though the human mind will ever remain very remote from 
the mind imagined by Laplace, yet this is only a matter of degrees, 
in some measure like the difference between a given ordinate of a 
curve and another immeasurably greater, though still finite, ordinate 
of the same curve. We resemble this mind, inasmuch as we con- 
ceive of it. We might even ask whether a mind like that of Newton 
does not differ less from the mind imagined by Laplace, than the 
mind of an Australian or of a Fuegian savage differs from the mind 
of Newton, In other words, the impossibility of stating and inte- 
grating the differential equations of the universal formula, and of 
discussing the result, is not fundamental, but rests on the impossi- 
bility of getting at the necessary determining facts, and, even where 
this is possible, of mastering their boundless extension, multiphcity, 
and complexity. 

DU Bois-Reymond, Limits of Natural Knowledge. 



CHAPTER XX 

NEWTON AND THE MOTOR FORCE OF THE 
WORLD MACHINE 

In the idle days of the long gone by, and especially with the 
revival of learning, men were wont to indulge in disputes, often 
lively, sometimes acrimonious, as to the superiority, especially 
in matters of the intellect, of the ancients or the moderns. 

Regard the matter as we may, among moderns at least the 
first place by a sort of common consent of mankind, without 
regard to nationality or calling, is awarded to Sir Isaac Newton. 
Without doubt, if one were asked to point to a single volume 
through all the ranges of literature, whether ancient or modern, 
which exhibits in the highest degree the powers of the human 
mind, one would fix without further thought upon Newton's 
Principia. It is amazing to reflect that it was as sheerly a 
product of chance as any event to which one might point. 

Various letters make it clear that Newton himself had no 
intention whatever of writing the Principia, though he was 
forty-four when he began it. But for the accident of a visit 
from young Edmund Halley in 1684, it is unlikely it ever would 
have been undertaken. Probably no book ever issued announced 
discoveries so great alike in number and importance ; had it not 
been for the importunate urgings of his disciple, they probably 
would have been buried among Newton's papers, perhaps to 
be exhumed as curiosities long after his death. Newton him- 
self would have been known to his contemporaries only as an 
amazingly ingenious mathematician who had invented fluxions, 
who discovered dispersion, and devised the reflecting telescope. 

His life, unruffled by tragedy, hardly by events, was, in an 

outward way, as commonplace as that of a railway president. 

He was born in the year of Galileo's death. He came up to 

Cambridge in 1660, the year of the Restoration, the year of the 

founding of the Royal Society, and while blind Milton, hunted 

by the partisans of the king, sought for a shelter for his head. 

253 



254 THE WORLD MACHINE 

The youth was rather more ignorant and uninstnicted than 
most country boys, even from the Lincolnshire whence he came. 
He was of simple farm folk ; his mother had done what she could 
to make him a good farmer lad like the rest, even to settling a 
small holding upon him. In the economy of events, fate had 
other uses for his wondrous brain. 

As a boy, like Galileo, he spent most of his time contriving 
curious bits of mechanism, and devouring everything he could 
get hold of upon such subjects. He made sundials, he made 
water-clocks, windmills, and curious kites. It is even said that 
he devised a four-wheeled carriage to be propelled by an occu- 
pant ; he may have constructed the first motor-car. They 
preserve a part of his sundial in the Royal Society. The thrifty, 
practical mother was in despair ; she appeals to the parish 
rector, and the rector finds Master Newton one morning under 
a hedge studying mathematics when he ought to have been 
marketing the farm's produce in town. Evidently the rector 
had sense enough to see that such a boy had good stuff in him ; 
and so on his advice Isaac gets a little schooling, and then is 
off to the university. Beyond a question he would have found 
his way eventually. As it is, it is a saving of time. 

He has a boy's devouring mind. At the Stourbridge Fair he 
invests in a book on astrology, and is vexed to find that he 
cannot understand a simple figure in trigonometry. So the 
next he buys is an English copy of Euclid ; and it seems 
to him childishly easy. Descartes' Geometry baffles him for 
a little ; in the end, his opinion of it is not very high ; note 
that he is then about twenty. Kepler's Optics fascinates 
him ; so does a book on logic. There is an entry in his diary 
that at this same time he read Wallis' works. The item is 
significant. Wallis was at this time the most celebrated mathe- 
matician in England. He had just put forth a treatise on 
Gravity and Gravitation. This may have been a subject of 
Newton's reflections when, a year or so later, the plague breaks 
up the university term and he goes back to Lincolnshire, his 
head in a violent ferment with all the new knowledge that has 
come into it. 

Already he has made three or four considerable discoveries : 
the binomial theorem, familiar enough now to every student of 
algebra ; the theory of infinite series which is to lead to fluxions 
— in our modern parlance, the differential calculus ; he has 



MOTOR FORCE OF THE WORLD MACHINE 255 

worked out the theory of the moon's halo ; he is deeply inte- 
rested in astronomy and optics. 

Precisely what set him pondering gravitation we do not 
know. In any of his own writings he makes no mention of 
the famous anecdote of the apple — that we owe to his niece, 
who told it to Voltaire, who embalmed it in the celebrated 
English Letters published a few years after Newton's death. 
The tree was there ; no doubt the apple fell. It is more likely 
that the germ of his discovery lay in his reflections over Kepler's 
laws, or in some passage in Wallis. Among the Portsmouth 
papers an old manuscript has been found giving his own account 
— giving, too, a glimpse of the amazing activity of his mind 
at this time. It runs : — 

" In the beginning of the year 1665 I found the method of 
approximating Series and the Rule for reducing any dignity of 
any Binomial into such a series. The same year in May I 
found the method of tangents of Gregory and Slusius, and in 
November had the direct method of Fluxions, and the next 
year in January had the theory of Colours, and in May following 
I had entrance into the inverse method of Fluxions. And the 
same year I began to think of gravity extending to the orb of 
the Moon, and having found out how to estimate the force with 
which [a] globe revolving within a sphere presses the surface 
of the sphere, from Kepler's rule of the periodical times of the 
Planets being in a sesquialterate proportion of their distances 
from the centres of their orbs, I deduced that the forces which 
keep the Planets in their orbs must [be] reciprocally as the 
squares of their distances from the centres about which they 
revolve ; and thereby compared the force requisite to keep the 
Moon in her orb with the force of gravity at the surface of the 
earth, and found them answer pretty nearly. All this was in 
the two plague years of 1665 and 1666, for in those days I was 
in the prime of my age for invention, and minded Mathematicks 
and Philosophy more than at any time since." ^ 

The account was written in after years, probably in his old 
age. It is not likely the discovery came to him with all the 
heavy armament of mathematical proof in which it appears in 

1 Quoted by Berry from the Preface to the Catalogue of the Ports- 
mouth Papers. 



256 THE WORLD MACHINE 

the Principia ; as a matter of fact the problem, if not the proof, 
was elementary. He had doubtless read Kepler's conjectures 
that the attractive force of the sun varies in some fixed pro- 
portion, simple, or as the square of the distance. Galileo had 
shown that under the force of gravitation the speed of a falling 
body increases with the square of the time. Perchance this 
same force of gravity, which the fall of the apple may have 
put in his mind, is the attractive force of the sun. It will be 
likewise the retaining force which holds the moon as well. The 
moon is about sixty times as distant from the centre of the 
earth as are we upon the earth's surface. If the force of gravi- 
tation projects outward to the moon, and it varies inversely as 
the square of the distance, then the earth's pull upon the moon 
will be just -^ws what it would be at the earth's surface. If, 
under the influence of this force, bodies fall in proportion as the 
square of the time, then the moon in a second will fall towards 
the earth a distance proportional to the square root of 3600 — in 
other words, at sixty times the distance it will faU as far in a 
minute as a body at the earth's surface does in a second. 

As the story goes, this lad of twenty-three tries it, taking 
the then accepted figures as to the diameter of the earth and, 
accordingly, the distance of the moon. It does not work out. 
It ought to fall sixteen feet per minute ; the calculation says 
less than fourteen. A man like Kepler, feeling the discovery so 
near, would have worked at it night and day, as he did at his 
Laws, for years and years. Newton was not metal of that temper. 
He put his calculations aside. He does not doubt that the 
law of duplicate proportion, as he caUs it, is involved ; but it 
may not be the whole explanation. Possibly Descartes' vortices, 
with visions of which his head no doubt is then full, may play 
some role ! Evidently for him TorricelH's experiment has yet 
not swept clean the spaces of the sky. It is strange that he 
thinks of the matter as of so little importance ; but in truth 
his head is then full of questions in optics. As soon as he gets 
a chance he will be bu5dng prisms and lenses, inventing tele- 
scopes and discovering the spectrum. Consider that aU these 
ideas come before he is twenty-five, and you will scarce wonder 
if he hardly sees the drift of some of them himself. 

Five or six years after, Picard made a more accurate measure 
of the size of the earth ; it appears that it was some years later 
still when, in London, Newton hears a discussion in which the 



MOTOR FORCE OF THE WORLD MACHINE 257 

new measures of the earth are related. He is stirred up to try 
anew. He goes back, rummages out his old papers, and begins 
again. As he foresees that the calculations will verify his surmise, 
his hand trembles so that he must lay down his pen. Still he 
does not publish his results. He has had annoying contro- 
versies with Hooke and others respecting the originahty of his 
invention of the reflecting telescope, his discovery of the com- 
position of white light. He seems to care little for publicity, 
and disputes disturb the pursuits of his peaceful life. Thus it 
is that four or five years later yet, when Halley comes down 
to inquire as to what will be the path of a body acted on by 
force of attraction varying inversely as the square of the dis- 
tance, Newton is able to reply promptly, " An ellipse." How 
does he know ? — " I have proved it." Halley travels back to 
London big with the news of the great discovery. Newton 
cannot find his papers just at the moment, but sends them a 
little later. A little later still, under the reiterate urging of 
Halley and the others, the Principia is begun. 

Such is the classical tale as you find it in Brewster or the 
encyclopaedias. The history of perhaps the most far-reaching 
single discovery in the whole range of scientific development is 
assuredly worth knowing, and correctly, if that be possible. We 
may believe with Rosenberger, whose learned and impartial 
monograph ^ considers the question at length, that the story of 
the apple is doubtless a myth ; likewise that the reputed discovery 
in 1665 was rather one of those ideas which boom into the 
teeming brain of youth, to be put aside or forgotten as easily 
as it had come. 

That Newton should be consciously so near the solution of 
so vast a problem, then give it up because the figures do not 
quite agree, does not fit with his character. His tenacity was 
extraordinary. Afterwards, to test out whether or no the law 
of gravitation was of universal apphcation, he tries with his 
own hands every kind of substance which he may lay hold of. 
Even in 1665 the measures of the earth, which are said to have 
led him astray, were out of date. It is scarcely believable 
that a man of his original and investigating mind would have 
been content to accept the erroneous figures without further 
question, when the error was so slight, and when he, moreover, 
^ Newton und seine Phystkalischen Principien. Leipzig, 1895. 

R 



258 THE WORLD MACHINE 

knew that many different estimates had been made. The truth 
seems to be that the law of gravitation had a gradual develop- 
ment in Newton's mind ; when the originahty of his discovery 
was called in question perhaps he yielded to an impulse, natural 
enough, to date it back as far as his earhest conjectures. 

There are doubtless few things in this world more hopeless 
than to attempt a just estimate of character, let alone that of 
Newton. We read with a smile the easy pages in which a 
Macaulay and his like lifts to his pedestal a venerated Whig 
and damns to perdition the hated Tory. Whoso will but 
attentively watch the flux and changes of his own interests, 
impulses, motives, deeds, from day to day, from year to year, 
from one period of hfe to another, will hardly be so ready with 
his judgments. When Newton's Principia appeared, Hooke 
promptly put in a claim to priority. It was the second of 
their encounters ; he was a batthng man. Newton was annoyed 
and disgusted. They had had an extended correspondence 
over planetary motion. Newton's work appeared years after 
Hooke had suggested, if he had not demonstrated, the central 
law which gave the book its fame. Hooke was aggrieved that 
it should contain no mention of his claim ; possibly Wren and 
Halley had something of the same feeling regarding themselves. 

In the controversy that followed, the character of Newton 
does not shine. He did not have that breadth of mind which 
enabled Kepler generously to applaud the discoveries of 
his friend Gahleo, nor that magnanimity which enabled 
Darwin to give to Wallace an equal place beside himself in the 
discovery of the origin of species ; the fact is rather painfully 
evident. In smaU charities, he was generous beyond his slender 
means, to relative or stranger. Towards his contemporaries 
he seems to us, at this distance — ^perhaps, as we may gather, to 
his friends as well, rather grudging. 

In after years a still more serious controversy, bitterly to be 
carried on by partisans long after his death, was to arise over 
his discovery of the calculus. Alike in this as in the others 
he discloses a human weakness to hold, unaccompanied, the 
centre of the stage. In a second edition, the more generous 
Halley induced Newton to make some recognition of Hooke; 
but he will minimise the claim of the latter so far as he may 
by dividing the recognition among all three — Hooke, Wren, and 
Halley too. 



MOTOR FORCE OF THE WORLD MACHINE 259 

It is quite probable that Newton did not realise at their 
just value the contributions of others. His own ideas, as we 
know, were icily clear ; he thought things out until every trace 
of turbidity was lost. Probably he had a very human im- 
patience with that confusion of thought which all of us find 
so troubling in the mental processes of others. Hooke's ideas 
never reached complete clarity. 

That a letter of Hooke's was the especial incitement which 
led Newton to take up his old calculations and conjectures and 
give to the law complete and irrefragable proof that will last 
with time, seems clear from Newton's own letters. That Hooke 
was deserving of much credit is certain. That the law would 
have been discovered within a very few years without a Newton 
is patent beyond question. But Hooke did not write the 
Principia — ^Newton did. In the Principia the law of gravita- 
tion is not put forth as a special fact — ^it is but a part of a vast 
scheme. What Descartes bravely attempted Newton achieved. 
With the aid of a single principle he disclosed our planetary or 
solar system as a vast yet simple mechanism, aU of whose motions 
were not merely fixed but calculable. This principle he appHed 
everywhere, aUke to the flight of the planets, the revolutions 
of their satellites, the flux and reflux of the waters of the earth. 
In the Principia, the human intellect reached for the first time 
a clear mental presentation of the workings of the world amid 
which its dream-like existence is passed. So far as the mechanics 
of the solar system is concerned nothing of consequence has been 
added since, and nothing has been taken away. It is this, and 
not simply the discovery or the proof of the law of mass-action, 
which is the true glory of Newton. 

Yet the discovery alone was a great deed. Its precise nature 
is often strangely befuddled. One may read in many a book 
that Newton did not discover gravity but simply the law of 
its action — that the force of gravity had been known for thou- 
sands of years. This is trifling. What Newton discovered, and 
demonstrated, was Attraction, not merely by the law but the 
fact, not merely the attractive force of the planets but of all 
matter whatsoever, from a molecule to a moon, from a grain 
of sand to the colossal mass of the sun. This discovery was 
wholly independent of gravity or any other consideration. It 
was, and might so have remained, complete in itself. So even 
does it appear to have been for a time in Newton's own mind. 



26o THE WORLD MACHINE 

The identification of the force of attraction with the well-known 
fact of gravitation constituted a second great step, a second 
discovery. It was simply an incident that they came together. 
Either the one or the other would have brought a large meed 
of fame. 

These two discoveries and the statement of their under- 
lying Law are the foundation of the Principia. 

It is not easy now to realise the vast stride forward which 
the publication of this single work represents ; it is equally 
difficult to separate out what was wholly Newton's own. It 
was not a large book, five hundred pages or so, so replete with 
diagrams that it looks like a geometry. The impression is 
further borne out by the fact that it is written in the style 
and language of Euclid, proposition succeeding proposition in 
an unbreakable chain ; it is the application of Euclid to the 
astronomy of the heavens. It is in no sense historical ; reference 
to the specific work of others is sparse ; it might readily be 
used as a textbook in a university. Without a precise know- 
ledge of the state of the science when it was written, one might 
readily believe that none, or all of it, was new. 

Newton had a mind that was at once comprehensive and 
synthetic, a gripping mind that made the whole cohere. It 
was he first of all who foresaw the consequences that followed 
from the law he had demonstrated. The moon is held by the 
earth, the satellites by Jupiter, the earth and other planets 
by the sun, in virtue of the force of attraction. This attraction 
varies directly with the mass of matter contained in each planet. 
He introduces, therefore, a new conception — that of mass as 
distinguished from mere weight. In the mind of Galileo this 
separation had not yet taken place. Newton saw and stated 
the logical inference — that is, that between every ultimate 
particle of matter in the universe there exists an inherent force 
or power which tends to draw them together, a power that 
grows less with the square of the distance which separates them. 
Consider that there was scarce a contemporary, or any one for 
some time after, who could grasp this simple, central truth — 
not Huyghens, nor Leibnitz, nor Jean Bernouilli, nor Cassini, 
great mathematicians all — the greatest of the time, and you 
wiU see how far this single mind outstepped its age. 

Newton was not merely the founder of celestial mechanics 



MOTOR FORCE OF THE WORLD MACHINE 261 

in the broadest sense — he was the founder of molecular mechanics 
as well. He gave, moreover, to general mechanics the last of 
the great conceptions needed for the perfection of the science ; 
he saw that action and reaction are equal. This, applied to 
planetary motion, gave a complete explanation of the curious 
perturbations of their orbital motion, long observed and mapped 
out, but until then inexplicable. It was not merely that the 
earth attracts the moon ; the moon in proportion to its mass 
attracts the earth and gives to its daily revolution the form 
of an eccentric. Could we watch it spin, we should see its axis 
wobble about a centre just as does the eccentric of a steam- 
engine. This same pull of the moon, exerted upon the unequal 
shape of the earth, gives to the direction of its axis the peculiar 
disturbance known as nutation, which will be discovered a few 
years later by Bradley. The combined pull of the sun and the 
moon, acting on this same uneven mass, produces the second 
displacement of the earth's axis, to which the precession of the 
equinoxes, discovered by Hipparchus, is due. 

Newton saw that the moon is attracted not only by the 
earth but by the sun as well ; hence its orbit will not be a true 
ellipse. By this means he explains and works out many of 
the disturbances of the motion of the moon, the variations in 
its inclination and the like. From the developments he had 
given to Kepler's laws he perceives that, knowing the distance 
of any body and the time of its revolution, he may calculate 
its mass in terms of the central body ; he calculates the mass 
of the moon, and, further than this, lays the foundations for 
a second means of verifying the calculated distance of the sun 
itself ; further yet, the mass of the sun. With this method, 
from careful observations of the variations of the planets from 
their natural paths as they react upon each other, it will one 
day be possible for Leverrier to determine at what distance 
the sun must be in order to produce the precise effects which 
it does. 

Newton laid the foundations for a knowledge of the true 
figure of the earth, and calculated that figure in its main details. 
He foresaw from the observed effects that the earth could not 
be a perfect sphere, that it was flattened at the poles, that its 
equatorial diameter was greater than the polar diameter, and 
that therefore the force of gravity at the poles was less than 
at the equator. He thus pointed out the path whereby in after 



262 THE WORLD MACHINE 

days mathematicians might work out the origin of the earth 
and of the solar system as well. 

He explained the tides. Poseidonius had done that in a 
way ; Newton gave the mathematical theory of the tidal flow, 
calculated how much was due to the moon, how much to the 
sun, explained why it was that the spring and autumnal tides 
were higher than at other times, by the conjunction of the 
attractive forces of the two bodies. Further consequences of 
his discoveries : he perceives that from their observed shapes 
it was possible to estimate the time of rotation of the planets 
— that is, the length of their " day." Thus Jupiter, despite 
its huge bulk, a thousand times that of the earth, has a much 
more violent rate of revolution ; its day is less than half our 
earthly day. 

And these are but the important matters of this kindling 
book. It was a wonderful advance ; you perceive that there 
was comparatively little left for those who were to come after. 
This is not saying that he made no mistakes ; they were as- 
tonishingly few. It is not sa5dng that he had wholly exhausted 
the subject ; Laplace, Lagrange, and many another were yet 
to come ; but the fact remains that in the essential theory 
neither discovery nor subsequent investigation has effected any 
radical change. The system of the world now taught to school 
children is the system of Newton. Perhaps the larger number of 
present-day works upon physical astronomy are a digest of the 
Principia. 

The work appeared within two years after it had been begun. 
Originally the Royal Society intended to defray the cost of its 
publication ; its funds ran low ; Halley put the book through 
the press out of funds from his own purse. He became thus 
not merely the godfather of the Principia ; it was his ward as 
well. The outlay involved a sacrifice ; it is pleasant to know 
that eventually he made well from his venture. It was written, 
of course, in Latin. Like Bacon, unlike Galileo or Bruno, 
Newton did not trust to his mother-tongue. England was then 
regarded by the rest of Europe as a half-barbarous land. Even 
Shakespeare was unknown. An enlightened continental as little 
thought of learning English then as he might think of acquiring 
Hungarian now. 

The Principia brought its author neither to the torture 
chamber nor the stake ; they gave him a Government post 



MOTOR FORCE OF THE WORLD MACHINE 263 

at a salary of £1500 a year instead. The times had wonder- 
fully changed. Revolution and counter-revolution, the wars of 
Catholics and Anglicans and Independents, had left England 
the freest country in Europe. The reign of Charles II. was a 
sort of Golden Age in English science. Weak and profligate 
monarch as he was, the kingdom prospered. The toleration he 
had encouraged was the downfall of his successor. The Principia 
came forth a year before the quietest revolution in English 
annals. Instead of Galileo's prison, when they began to realise 
Newton's greatness and found that he was poor, they gave him 
a position first of Warden, then of Master, of the Mint. The 
Royal Society soon elected him its president — ^was proud to 
retain him there through four-and- twenty years. He enjoyed 
his fame ; the anchorite and recluse became a good liver ; death 
did not reach him until the ripe age of eighty-five. They 
throned him in Westminster Abbey ; peers carried his pall. It 
was a singular contrast from the fate of his great forerunner, 
who had died the year of Newton's birth, banished from associa- 
tion with his fellows, imprisoned and disgraced, at first denied a 
decent burial. 

Yet the work of Newton was far more atheistical than that 
of Galileo. Leibnitz, then rising to his place as one of the most 
widely read philosophers of Europe, declared that " Mr. Newton 
robs the Deity of some of his most excellent attributes, and has 
sapped the foundations of natural religion." No matter ; it is 
a Cambridge divine who translates the Principia into English 
and becomes one of its warmest defenders. There arose in the 
English Church a sort of school, bent on establishing a new 
theology, based upon the new conception of the world as a 
mechanism. You see a last expression of it in the famous work 
of Paley. 

Curiously enough, in this development of his own philosophy 
Newton took no part. He spent a goodly share of his remain- 
ing days writing theological dissertations and tracts. They 
betray no gleam of the new light he himself had brought. 
Coming from such a mind, they are amazing products ; they 
would be inexplicable if we did not know of the unhappy fatality 
which befeU him shortly after the publication of the Principia 
and to all intents closed his scientific career. There seems to 
be little doubt or question that the strain which the production 
of the Principia involved told heavily upon Newton's strength. 



264 THE WORLD MACHINE 

Few men ever had greater powers of absorption in their work. 
In his waking hours he was hterally lost in calculation and 
thought. Often he forgot to eat, sometimes to finish dressing 
in the morning after he had arisen. 

This intense application, evidently, brought on an illness. 
For a time there is little doubt that his mind was clouded. 
There was a natural effort, alike on the part of friends and 
subsequently by admiring biographers, to conceal or minimise 
this. His own letters and the testimony of those who visited 
him leave no question as to the fact. He recovered his health, 
but never the vast powers of his intellect. At forty-five his 
work was done. Years after, with the help of younger men, he 
brought out a second edition of the Principia. His work on 
Optiks was not published until 1704 ; it had been written 
long before ; the delay was due purely to his controversy with 
Hooke. 

The Principia had appeared on the eve of a dramatic revo- 
lution in the political world ; in its own world it produced none. 
The history of science is rarely spectacular. One might readily 
think that such a work and such a man would have given rise 
to a great school which for a long time after would have en- 
sured the precedence of England in the scientific advance. They 
did nothing of the sort. One wonders less, when considering 
this, that the bold theories of Aristarchus should have seemed 
to make so slight an impress in the Alexandrian days. For a 
century after the Principia there is hardly a single great dis- 
covery in English astronomy. Newton's work was taken up, 
carried on to the last perfection of its details, by the mathe- 
maticians of Germany and France. 

Highly regarded in England, it was yet forty years before 
the Principia began to take effect on the Continent. Near a 
half-century after its appearance, the French Academy of 
Sciences, the most considerable body of its kind then existing, 
was awarding a prize for the paper in which the movements 
of the planets were explained on Descartes' theory of vortices 
— tourhillons. And the award was to Jean Bernouilli, one of 
the three or four foremost mathematicians of the day. 

But what the impervious academic mind could not under- 
stand, the freer mind of the laity might. So it was to a lay- 
man, to the celebrated Voltaire, largely, that Newton's European 
fame was due. A refugee in England, that myriad-minded 



MOTOR FORCE OF THE WORLD MACHINE 265 

prestidigitateur had learned to admire English institutions and 
English thinkers. When, with a comfortable fortune acquired 
in clever speculation in corn, he was allowed to return, it was 
to publish his celebrated Lettres Philosophiques sur les Anglais^ 
and the Epitome of the Newtonian philosophy. European 
thought was still dominated by the fantasies of Descartes. In 
the battle royal that followed the militant pen of the Newtonian 
protagonist found an able lieutenant in his charming companion 
at arms, the learned and amiable Marquise du Chatelet. It 
was the latter who translated the Principia into French, adding 
thereto a highly creditable commentary of her own. 

Newton's neglect or disregard of feminine society or associa- 
tion during his life appears to have been complete. It was his 
fate to be introduced to the larger audience of Europe through 
the pen of one of the most interesting adornments of her sex. 
The volume of Madame du Chatelet to-day commands a con- 
siderable price, testimony to one of the rare episodes in philo- 
sophy touched with any colour of romance. 

As to the judgments of Newton's immediate contemporaries, 
it scarce needs be said, since the fact is universal, that their 
rejection of the ideas of the Principia was all but unanimous. 
Strangest of all was that of Huyghens, whose law of centrifugal 
force was one of the strongest weapons in the Newtonian argu- 
ment. It was simply the old story ; for mystery Newton had 
substituted simplicity and law, and to mystery purblind authority 
will cling so long as it may. But soon the generation of re- 
jection will pass ; a newer generation will come which accepts. 
In another century a man who doubts what the greatest mathe- 
maticians, thinkers, and philosophers in Europe had doubted 
or flouted will be regarded simply as a fool. 

What Newton taught will not cease to be the truth so long 
as the world lasts. Unto him it was given to unveil a secret 
of the universe. Until Newton came man could scarce have 
any rational conception of the world into which he is born. 
The event was worthy of the sumptuous phrase it found in 
the epigram of Pope : — 

" Nature and Nature's laws lay hid in Night ; 
God said, Let Newton be, and all was light." 

There yet remained an absorbing mystery which must be 
solved before the description of the celestial machine was com- 



266 THE WORLD MACHINE 

plete, before all of its parts and its workings could be accounted 
for. It seems slight enough to our modern time, rubbed so 
clean of der Sinn fur das Wunderbare, " the sense of the miracu- 
lous," which was the native hue of the mind of our forbears. It 
did not seem so then. — What were the argent flames, sometimes 
soft and nebulous, often dazzling and vast, which come by times 
across the quiet heavens ? 



CHAPTER XXI 

HALLEY AND THE MESSENGERS OF 
THE GODS 



The human mind enjoys to-day an enormous possession of ideas, 
heaped up, selected, sifted out by the centuries. The multitude 
of men have disappeared without contributing to this store a jot. 
Those who have had the fortune to add something, to leave some- 
thing, should have their part in the glory and the recognition which 
is their due. 

Bailly, Histotre de rAstronomie Moderne. 



CHAPTER XXI 

HALLEY AND THE MESSENGERS OF THE GODS 

As we wander nowadays among the broken pillars and moulder- 
ing columns which tell of the grandeur that was Rome, the time 
seems long. Yet may we hardly doubt that, could we be 
transported back to the days when these were palaces, arches 
and temples of marble, we should find a civilisation and a 
society which in its polish, its elegance, its urbanity of manners, 
its scepticism and audacity of thought, would differ from our 
own only in the minor essentials of a different fashion of dress, 
of speech, of dining, and their like. Some things have changed, 
however, and one of these is the singular belief — singular now 
to us — in signs, in portents, haruspices, good and evil omens. 

Cicero was a highly enlightened man, dipping into all the 
science of his time, writing out his views in a sensuous and 
flowing Latin whose charm the intervening centuries have not 
dimmed. On fate he wrote like a philosopher ; on divination, 
the reading of the future from the entrails of chickens or the 
turn of a sieve, he wrote with a faith that one might expect to 
find in a fishwife or a child. He is hurt because the great 
Democritus, whom he so much admires, should treat the subject 
so lightly ; he adduces a whole row of names of the eminent 
and the learned to indicate how wrong it is of the Abderan 
sceptic to consider so little a belief which had been unquestion- 
ingly entertained by so many excellent minds. The views of 
Cicero were but the refinement of the gross superstitions which 
then dominated not merely the cultured society of Rome, but 
the whole world. You perceive it in many ways. 

The death of Caesar was a momentous event ; by common 
suffrage he was voted a god ; the shows and pageants of earth 
seemed too slight to do honour to the passing of this god-like 
man. As heralding his demise, does not Horatio tell us in the 

play:— 

" The graves stood tenantless, and the sheeted dead 

Did squeak and gibber in the Roman streets." 
269 



270 THE WORLD MACHINE 

Shortly after his assassination a flaming apparition visited the 
sky, a vast and graceful trail of light. It shone so brilliantly 
that it could be seen for several hours before sunset. It held 
its portentous way in the heavens for eight days, then dis- 
appeared. Small wonder that the Romans should have given 
to this effulgence the name of the Julian Star, and regarded it 
as a celestial chariot sent to convey the soul of Caesar to the 
skies. 

These apparitions were not uncommon ; the terror they 
inspired was sometimes beyond measure. In the year 1456 
came one of unwonted splendour. Constantinople had just 
fallen before the invading arms of the Saracen. " The appari- 
tion," says Draper, " was considered a harbinger of the vengeance 
of God, the dispenser of the most dreadful of his retributions, 
pestilence, famine, and war." By order of the Pope, aU the 
church bells of Europe were rung to scare it away ; the faithful 
were commanded to add each day another prayer. As they 
said their Ave Maria, they joined to their supplications to the 
Holy Mother the words : " Lord save us from the devil, the 
Turk, and the comet." 

In the year 1910 one of these flaming messengers will appear 
in the sky ; the time of its coming will be calculated perhaps 
to a day. The faithful will not fall upon their knees ; no new 
prayers wiU be said ; the church bells of Europe wiU not ring. 
It will not be regarded as a portent of famine or war ; if the 
greatest of Hving statesmen dies upon its approach, it will not 
be thought of as a special vehicle to waft heavenward his soul. 
What has wrought the change ? 

The answer may be a little technical, but we may say with 
some approach to accuracy, Newton and his law of attraction. 
Up to Newton's time the comet was still a mystery. Its appear- 
ance inspired an instinctive dread in even the stoutest hearts. 
In the year 1680 came a wonderful specimen. Newton watched 
it rush downwards towards the sun, spin round about it in an 
abrupt turn, then rush away again and disappear from sight. 
He did not tremble ; he observed. Then he calculated. Newton, 
despite his theologising predilections, had a very concrete and 
material sort of mind ; he reflected that if this apparition were 
of a material nature it must be subject to the influence of gravita- 
tion and obey the formula whose secret he had seized. It would 
then move in one or other of the conic sections, as do all projec- 



THE MESSENGERS OF THE GODS 271 

tiles ; the sun would be in one focus, and following out Kepler's 
law, its radius vector would cover equal areas in equal times. 

The observations made from different points were carefully 
examined ; the path of the orbit, so far as might be, was plotted ; 
it answered in every way to Newton's anticipations — it obeyed 
a law of expectancy. Thereafter the mystery of the comets was 
gone. From that time onward their paths and the date of their 
return, should their paths be of such a shape as to bring them 
back, was simply a matter of mathematical reckoning. Newton 
found that the comet of 1680 moved in an orbit so near to a 
parabola that its period was some hundreds of years at the 
least. Later observations tended to indicate that its path 
might be that of a very much drawn out ellipse. If this be 
true, it will return in some three centuries, probably around 
the year 2255. If this idea of its periodicity is correct, it had 
appeared previously in 1106 and in 531 a.d. ; it would be the 
same which bore Caesar to his resting-place among the gods. 

Newton was not the first to suspect that the comets might 
move in orbits like planets. Kepler had so surmised. In his 
day there came a very splendid comet, afterwards to acquire 
an especial significance as the first of these apparitions whose 
orbit was reckoned and its predicted return realised. In the 
year 1618 there were three more. Kepler made a book about 
them, speculating concerning their nature in his wild and un- 
restrained way ; but in this as in so many others, coming 
wondrously near to the truth. His master, Tycho, had been 
deeply interested in the subject, had likewise written a book 
upon them. It was Tycho, indeed, who first showed from 
accurate observations that these apparitions are not generated 
within the earth's atmosphere, as had so long been supposed, but 
that they come from beyond the orbits of the planets. It was 
his boast that by means of his observations he had destroyed 
for ever the seven- and-seventy solid crystalline spheres which 
the ancient imagination had invented to account for the move- 
ments of the planets and the stars. 

Tycho did not see that they travel in orbits, but he held 
firmly to the view that they were celestial and not terrestrial 
bodies. Following him, Kepler accounted for their appearance 
and disappearance by supposing that they moved in straight 
lines ; having once passed near the earth, they would then 
recede indefinitely into space. He did not seem to think it 



272 THE WORLD MACHINE 

worth while to test out his theory by actual observation. Had 
he done so he might easily have anticipated Newton. But he 
reflected upon the fact, noted by Fracastor and others, that 
the tails of comets point always away from the sun ; he ex- 
plained this on the supposition that the tail is formed by rays 
of the sun which penetrate the body of the comet and carry away 
with them some portion of its substance. 

We do not think of hght as a hail or bombardment of ex- 
tremely minute corpuscles as Kepler did, and Newton too ; but 
with this difference, his theory was in close coincidence with 
our modern ideas. Within the last two or three years it has 
been shown that, as Maxwell predicted, light may exert a 
pressure, even though it be a form of motion and not a substance. 
It is apparently this pressure which swings the tail of the comet 
around so that the body of the comet usually points towards 
the sun. 

Galileo got no further. But two years after the appearance 
of the great comet studied by Newton, came another. From 
careful observations, Halley was able to compute its orbit in 
accordance with Newton's principles. In 1705 he too published 
a work on comets, in which no less than twenty-four orbits were 
calculated. He had been struck by the resemblance between 
the paths described by the first of these and one of seventy- 
five years before. Looking through the old records, he found 
mention of another in 1531 and again in 1456 ; he conjectured 
that they were perhaps all of them but different appearances 
of the same comet, revolving round the sun in a period of about 
seventy-five and a half years. Inspired by this coincidence, 
he stepped out into space, as it were, and watching its path 
with the eye of the imagination, predicted its return in 1758. 

Truly a splendid flight of the mind it was, thus to throw off 
the heavy shackles which tie us down to the here and now, 
and sweep through the centuries, backwards through history, 
forward through history yet unmade ; but his faith was justified. 
Not only did the comet reappear, but long after the soul of 
Halley had followed that of Caesar, in the common way of 
all our human kind, the mathematician Clairaut, utilising the 
materials he had left, calculated its return within a month. It 
returned again in 1835, its appearance this time being predicted 
within three days. The existence of the planet Uranus, which 
had been a disturbing influence in the previous calculations, 



THE MESSENGERS OF THE GODS 273 

had in the meantime been discovered and its effect measured. 
This is the comet which in all probabihty will return again 
in 1910. 

Four others are now known which revolve in an elongated 
ellipse like Halley's comet, with a period of between seventy 
and eighty years ; about twenty-five are known with lesser 
periods, and perhaps as many more with periods of over a 
century. Altogether the paths of upwards of two hundred 
comets have been plotted in whole or in part. So much, then, 
is known, that they all obey the same laws as the planets ; 
they are therefore material substances and under the domina- 
tion of a simple mechanical law. So far from being a stumbling- 
block towards the acceptance of the theory of attraction, they 
have been a help to show its universal application. Their 
appearance is to-day no more of a mystery than the daily and 
hourly flight of the earth through space. 

Whatever be the substances which compose the comets, they 
are in an exceedingly tenuous state. Their tails are often millions 
upon millions of miles in length ; sometimes they reach clear 
across the orbit of the earth. This implies necessarily an 
enormous amount of matter of some kind ; nevertheless it is 
so thinly distributed that very often on a clear night we may 
look quite through these nebulous masses and see the stars 
shining in their customary way. Even the slender flicker of 
light from far-distant suns suffers little obstruction in passing 
through them. 

Moreover, it is now known that the earth has twice shot 
through a comet's tail ; so little disturbance did it create that 
the fact was only made clear from calculations after the event. 
Still again, the comet of 1843 swept so swiftly about the sun 
that it had made the turn from one side to the other within a 
couple of hours. In order to accomplish such a feat the speed 
must have been something so enormous, that beside it the 
earth, at nineteen miles per second, would seem to creep. And 
this was simply for the head of the comet ; if the tail of the 
comet, which was unusually long, followed the usual observed 
actions of comets' tails and pointed away from the sun through- 
out the curve described by the head, the rate at which its 
particles moved would have been simply inconceivable. 

The obvious inference, therefore, is that the tail is not a 

s 



274 THE WORLD MACHINE 

permanent part of the comet at all, but that, as Kepler had 
partly guessed, it is simply a stream of matter driven off from 
the head, or nucleus, by the pressure of the sunlight. It would 
be more tenuous than any mist or vapour we may conceive. 
It would bear perhaps the same relation to the comet proper 
as the thin line of smoke and flaming cinders thrown out by a 
flying locomotive to the locomotive itself. This inference seems 
fairly substantiated by the fact that the tail only appears as the 
comet approaches the sun ; when at a great distance the comet 
represents only an indistinct patch of nebulous light. Finally, 
if this view be correct, we should expect to find that the short- 
period comets which sweep around the sun every few years or 
so would, through a long series of observations, show a diminu- 
tion in their volume, owing to the quantity of matter driven 
off into the tail and left in space. This is precisely what has 
been found. 

It remains, then, merely to find out the nature of the 
nucleus, or head, and the mystery of these fiery portents 
is completely solved. The question has a double interest from 
the fact that it may shed some light upon the stuff of which 
the universe is made. While the great majority of the comets 
appear to describe closed orbits, some certainly do not. They 
are simply drawn into our solar system by the chance of having 
come within the clutches of solar attraction in their flight through 
space. They appear but once, and then are gone for ever. 
Could we but know their chemic composition, we should know 
a little more than we do of worlds beyond our own. It is only 
within the last thirty or forty years that the clue has come. 

It was unexpected in its simplicity. Watching the heavens 
by night, the eye is often thrilled by the spectacle of a gorgeous 
flash of hght which we are wont to call a shooting-star. Some- 
times, as we know, these shooting-stars come in a kind of a shoal ; 
we speak of these as meteoric showers. As a rule the headlong 
dash of these bodies through the earth's atmosphere generates 
so fierce a heat that they are dissipated into vapour, and their 
substance is left to float about in the air as a part of the dust 
which gives the sky its wonderful hue of blue. Eventually it 
settles down to the earth ; and this, it seems likely, is the origin 
of the fine metallic dust which will cover snow-fields even of far 
northern cUmes, where the atmosphere is of the purest and where 
smoke and dust seem almost excluded. This surmise has ap- 



THE MESSENGERS OF THE GODS 275 

parently been confirmed in a very simple way. Merely by 
melting down a quantity of long exposed snow, in filtering it 
out are found once molten globules of iron and other materials, 
as well as larger bits. 

Occasionally, however, there comes a shooting-star of great 
bulk which plunges through the atmosphere like a glowing ball, 
to bury itself in the earth with a loud report. These are the 
great meteoric stones, some of which have been known to weigh 
many tons. Fine specimens are usually to be found in the 
natural history museums. They may be assayed or analysed 
chemically, precisely like any other bit of rock. They contain 
no new kind of material, no element which is not found upon 
the earth. If therefore they come from the far depths of space, 
the material of the universe is all the same. 

It was a splendid surmise. But what reason have we for 
supposing that they do come from outside our solar system, 
and what have they to do with comets ? The curious answer 
is that these meteorites or shooting-stars are simply little 
comets ; the great comets seem merely vast swarms of meteorites. 
If the comets come from beyond the confines of our system, 
the meteorites probably do the same. We have fair evidence 
that with some of them this is the fact. 

It is strange how little interest the subject seemed to have 
inspired until the discovery made by Professor H. A. Newton, 
of Yale University in America. Tracing out all the records of 
meteoric showers which he could find. Professor Newton arrived 
at the conclusion that some of these showers at least had a 
definite period. In particular, there seemed one shoal of 
meteors through which the earth passed, in November, once in 
every thirty-three years. He could find an apparent record of this 
swarm back to the year 599 a.d. Their last appearance, when he 
had counted them up, was in 1833. Following the path of Halley, 
he boldly predicted their return in 1866 or the year following. 

They came just as he had calculated. They did not appear 
again in 1899, but came straggling along two or three years 
later, and the display was far less brilUant than in '66. It 
seemed as if the shoal had to some extent been broken up. 
Nevertheless there seemed no mistaking the fact that these shoot- 
ing-stars move in an orbit like the planets. When this especial 
shower appears, its radial and axial point in the heavens is in the 
constellation Leo ; hence their name of the November Leonids. 



276 THE WORLD MACHINE 

The swarm is enormous in extent, almost countless in 
number. The display lasts for four or five hours ; this means 
that the earth, shooting along at 70,000 miles per hour, requires 
this length of time to cover it from side to side. Its velocity 
of motion has been calculated ; it comes out, at least in the 
earth's atmosphere, at twenty-five miles a second ; yet it takes 
nearly three years for the whole swarm to pass a given point. 
So, in a rough way, we may compute its size. The breadth of 
the swarm is greater than the distance from the earth to the 
moon ; if its speed in space is the same as near the earth, its 
length is many times the distance of the earth to the sun. 
Perhaps if we conceive a shoal of fish, some large, some smaU, 
some not so big as tadpoles, rushing along at twenty miles per 
second — a shoal perhaps several hundreds of millions of miles 
in length — ^we may form some picture of how they might look, 
could we see them as a whole. We cross the orbit of this swarm 
every year, yet it is so tilted to that of the earth that it is only 
once in thirty-three years that we encounter this enormous mass. 

When the orbit of the Leonids was laid down in a diagram, 
it was found to bear a close resemblance, in its general form, 
to that of comets Hke Halley's, which move in a very long 
ellipse. The instant conclusion was that there is an intimate 
relation between these meteoric swarms and the comets. This 
became a practical certainty when the paths of four different 
swarms were computed and found to agree closely with the 
paths of known comets. 

One of these comets had an extraordinary history. This 
was Biela's, a carefully observed telescopic apparition, making 
its round of the sun once in six years. It was duly observed 
on several successive returns ; but along about 1846 it was 
calculated that, at its next revolution, it would come very near 
to Jupiter. Naturally there was a great deal of wonderment 
as to what would happen to Jupiter, or the comet. It was the 
idea that we might see, as on a stage, the representation of 
what would happen, in case, as the old-time terror had so long 
anticipated, a comet should strike the earth. 

When it came again, it was seen that Jupiter was not de- 
stroyed ; but the comet itself seemed to have been cut in two. 
Both portions of the split-up comet appeared again in 1852 ; 
but in 1858 it was nowhere to be found. The astronomical 
authorities duly sent out notices that kindly disposed individuals 



THE MESSENGERS OF THE GODS 277 

might give any information they might be possessed of as to 
the whereabouts of the lost comet. It never reappeared. 

But the orbit of the comet was well known, and it was cal- 
culated that in 1872 the earth would just about cut across the 
point where the missing comet ought to appear. The night 
came, but no comet. What did come was a shower of shooting- 
stars. The same thing happened in 1885. There seemed no 
mistaking the fact that Biela's comet had gone to pieces ; it 
had simply degenerated into a meteoric swarm. It does not 
stand alone. Brooks' comet of 1889 was found to be accom- 
panied by three smaller companions, and as this comet often 
passes very near to Jupiter just as did Biela's comet, it seems 
likely that it is undergoing the same disintegration. 

Probably the same thing is going on with several others ; 
it is yet too early to know. The subject is new ; but there 
seems httle reason now to doubt that the meteorites are simply 
comets in decay, the stragglers of a lost battle, and that on the 
other hand the comets are vast swarms of these meteoric stones. 
The evidence of the spectroscope makes this a practical certainty. 

It is of interest to know that, at least in one instance, it 
seems probable that these meteoric swarms, like some comets, 
have been incorporated into our system within historic times. 
The great French mathematician Leverrier, in calculating the 
orbit of the November meteors, found that it was an oval ex- 
tending out beyond Uranus. The paths of the comets are 
disturbed by the attractive influence of the planets ; calculating 
back the past positions of the Leonids, Leverrier came to the 
conclusion that under the influence of Uranus the form of its 
orbit had been completely changed. Very hkely it once de- 
scribed a parabola about the sun ; it was, therefore, in all 
probabihty a comet moving through space which closed within 
the grip of the sun or of one of the outer planets. It would 
have been torn to pieces by their combined influence, pulled 
and hauled about until it had lost its great velocity, and was 
but the rags and tatters of its former self. On Leverrier's 
calculations it entered the solar system a century or so after 
the death of Caesar, that is, in the year 126 a.d. It was a 
beautiful piece of computation, not so brilliant perhaps as 
another which we shall meet with soon, but surely calculated 
to excite admiration for the perfection of the astronomer's art. 

But the study of meteorites and the paths of the swarms 



tij^ THE WORLD MACHINE 

was to lead to something more than a striking exhibit of the 
powers of calculation. The bombardment of the earth by the 
meteorites is incessant ; we see them, of course, only at night ; 
but the hail of these bodies, large and small, continues through 
the day as well. One careful series of coimts was made which 
indicated that the number may reach fifty or sixty thousand 
in each twenty-four hours, perhaps twenty millions in a year. 
Most of them, of course, are very small. Taking an average. 
Professor Newton, who virtually created the modern view of 
meteorites, calculated that the earth in its flight sweeps up a 
hundred, or it may be several hundreds of tons of meteoric 
matter per day. It is not a great deal, perhaps, set against 
the vast bulk of the globe. In a million years, perhaps, they 
would not at this rate cover the whole surface of the earth 
with a layer more than an inch thick. But their number pro- 
bably is growing less year by year ; it may have been far greater 
in the long ago. If we prolong our vision far backward, through 
geologic time, through hundreds of millions of years, we see 
that the cumulative effect must have been great. 

Moreover, just as the comets and meteoric swarms may be 
pulled apart, disintegrated by large bodies, so evidently they 
may come together, may coalesce, may be integrated among 
themselves. Instantly in the reflecting mind comes the ques- 
tion : is it from these that worlds are born ; is it thus that through 
the aeons, suns and planets grow? Though such an idea has 
come to more than one mind, it remains as yet rather an in- 
teresting possibiHty than a tenable theory. 

Step by step the mystery slips away. With the terror of 
the comets a large part of it had gone ; not all. Back in 
Newton's and in Halley's time there was one they must have 
pondered oft. It brought no terror ; it was a puzzle none the 
less. What is light ? Does the effulgence of the sun, the 
radiance of the stars, flash to us in no lapse of time ? Can its 
traverse of space be instantaneous ? 

So it seemed. And yet the fact was unthinkable, just as 
the fact of gravitation is still. Already one young observer had 
seen that some curious appearances could not be so explained. 
Until the matter was cleared up, certain avenues to investigation 
were blocked. Science cannot deal with infinities. The path 
to the solution was devious. 



1 



CHAPTER XXII 

ROEMER AND THE PROOF OF THE 
EARTH'S MOTION 



Whether the sun predominant in Heaven 

Rise on the earth, or earth rise on the sun ; 
He from the east his flaming road begin, 

Or she from west her silent course advance 
With inoffensive pace that spinning sleeps 

On her soft axle, while she paces even. 
And bears thee soft with the smooth air along ; 

Solicit not thy thoughts with matters hid ; 
Leave them to God above. Him serve and fear. 

Paradise Lost, viii. (1667). 



CHAPTER XXII 

ROEMER AND THE PROOF OF THE EARTH'S 
MOTION 

With the demonstration of the law of attraction, the triumph 
of the Coppernican theory seemed complete. Tested in every 
direction in every land where observations were carried out, 
the ideas of Newton were subjected to inquiry only to be con- 
firmed, their application extended. There seemed no flaw, no 
difficulty. And yet a difficulty remained. It was the same 
that had met Aristarchus and Coppernicus, that had baffled 
Galileo. It was left unsolved by Newton or by any contem- 
porary. That was the unchangeable position of the fixed stars. 

To escape the difficulty, sometimes like the ancients men 
had imagined a crystal sphere wherein the stars are fixed like 
so many nails studded in a wall. Galileo considered this, but 
in his third Dialogue he said : — 

" Still I do not believe that all the stars are scattered over a 
spherical surface at equal distances from a common centre ; but 
I am of the opinion that their distances to us are so various 
that some of them may be two or three times as remote as others, 
so that when some minute star is discovered by the telescope 
close to one of the larger, and the former is yet highest, it may 
be that some sensible change may take place among them." ^ 

In the century that followed the invention of the telescope 
no such change could be detected, and a truly marvellous pre- 
cision had been attained. The accuracy of observations had 
been carried down from limits of error of the fraction of a degree, 
obtainable by the ancient instruments, first to a minute, finally 
down to a few seconds. The telescope with which Galileo had 
discovered the " little world " of Jupiter, magnified only seven 
diameters. AU his great discoveries, as we have seen, were 
made with a telescope which did not magnify beyond thirty- two 
diameters. Within fifty years Auzout had constructed colossal 

^ Dialogues on the Two Great World Systems, III. 
281 



282 THE WORLD MACHINE 

telescopes without tubes, 320 feet long and magnifying 600 
times. So far from reducing the distance of the stars with the 
new instruments, they seemed but to recede farther and farther 
into the depths of space. So long as it was possible to measure 
angles with accuracy down only to a minute of arc, as in Tycho's 
day — that is to say, an arc the 20,000th part of a circle — this 
meant merely that the nearest of the stars must be nearly 3500 
times the mean distance of the earth from the sun. Already 
it was taxing the limits of creduHty. The sun, eighty milhon 
miles or more away ; the starry firmament, 3500 times eighty 
millions ! It was unthinkable ; it was almost unbelievable. 

The new instruments carried these distances almost to infini- 
tude. The little wire-netting which Gascoigne had stretched 
across the focus of the telescope made it possible to measure 
down to a second. The lower limits of stellar distance rose to 
200,000 times the distance of the sun when this degree of pre- 
cision had been reached. Yet even with an instrument capable 
of disclosing this minute variation in the position of a star, 
no certain change like that predicted by Galileo could be found. 
One astronomer after another believed that a parallax, a change 
of position, could be observed. One after another their results 
were discredited or disproved. Such was the state of the science 
when Newton was borne in honour to Westminster Abbey. So 
it was to remain for more than a hundred years thereafter, 
that is to say, down to the second or third decade of the nine- 
teenth century. 

Slight wonder, then, if some shadow of a doubt stiU remained, 
slight marvel if some of those whose instincts of conservatism 
made them still cling to the ancient beliefs, might hope that 
some observation, some event might come which should reveal 
this new and godless system of the world £is the baseless fabric 
of a dream. Inspired by the magnificent conquests which a 
few decades of the telescope had achieved, the astronomers 
did not despair ; they went on observing. As many times 
happens in the history of invention and discovery, they found 
not what they sought, but great things none the less. A 
Columbus in the quest of India reveals the new world ; the 
observers in search of stellar parallax disclosed the finite velo- 
city of Ught. With this came the proof which sets the motion 
of the earth beyond intelligent doubt. 

Probably the most ancient of physical investigators had at- 



THE PROOF OF THE EARTH'S MOTION 283 

tempted to solve the problem as to whether or not the trans- 
mission of light is instantaneous. Every schoolboy has observed 
the difference in the propagation of light and sound. The flash 
of a rifle from a distance is seen long before we hear the report. 
It required tests of no great delicacy to approximately measure 
the speed of sound. The phenomena of light had been studied 
from the most ancient times ; Ptolemy of Alexandria had left 
a treatise upon the subject. The laws of reflection were known 
to his day ; refraction, the bending of Hght as it passes through 
media of varying density, had been observed closely by 
Poseidonius, by some of the Arabians, and by Friar Bacon. 
With the tremendous awakening of physical investigation which 
followed the discovery of America, and especially with the in- 
vention of the telescope, the subject was taken up anew by 
scores of eager minds. Lord Bacon fumbles with it, as with 
so many other of the current ideas of the time. There is a 
passage in the Novum Organum that may be worth the quoting, 
aUke cis an excellent example of the later Bacon's stumbling 
logic and confused thought, and of the notions prevalent in 
his day. It runs : — 

"... The flight of the musket ball is too swift to allow 
an impression of its figure to be conveyed to the sight. This 
last instance, and others of a like nature, have sometimes ex- 
cited in us a most marvellous doubt, no less than whether the 
image of the sky aud stars is perceived as at the actual moment 
of its evidence, or rather a little after, and whether there is 
not (with regard to the visible appearance of the heavenly 
bodies) a true and apparent time, as well as a true and apparent 
place which is observed by astronomers in parallaxes. It ap- 
peared so incredible to us that the images or radiations of 
heavenly bodies could suddenly be conveyed through such im- 
mense spaces to the sight, and it seemed that they ought rather 
to be transmitted in a definite time. 

" That doubt, however (as far as regards any great difference 
between the true and apparent time), was subsequently com- 
pletely set at rest, when we considered the infinite loss and 
diminution of size as regards the real and apparent magnitude 
of a star, occasioned by its distance, and 'at the same time 
observed at how great a distance (at least sixty miles) bodies 
which are merely white can be suddenly seen by us. For there 



284 THE WORLD MACHINE 

is no doubt that the light of the heavenly bodies not only far 
surpasses the vivid appearance of white, but even the Ught of 
any flame (with which we are acquainted) in the vigour of its 
radiation. 

*' The immense velocity of the bodies themselves, which is 
perceived in their diurnal motion, and has so astonished thinking 
men, that they have been more ready to believe in the motion 
of the earth, renders the motion of radiation from them (mar- 
vellous as it is in its rapidity) more worthy of belief. That 
which has weighed most with us, however, is, that if there were 
any considerable interval of time between the reality and the 
appearance, the images would often be interrupted and confused 
by clouds formed in the mean time, and similar disturbances of 
the medium. Let this suffice with regard to the simple measures 
of time." 

It should be needless to remark that again the italics in- 
dicated are not Bacon's. While the prophet of the Great 
Instauration was balancing speculations, the more practical- 
minded Galileo was attempting a crude measure of the actual 
speed of transmission. Others perfected his methods ; the 
velocity still seemed infinite, the passage of light from star 
to earth instantaneous. 

So it appeared to Descartes ; so it remained until a curious 
observation by a young Danish observer, Olaus Roemer. While 
Cassini is making a correct measure of the distance of the sun, 
revealing the enormous breadth of the earth's orbit, this young 
Dane is taking note of an extraordinarily minute but certainly 
observable difference in the times of revolution of one of Jupiter's 
moons. It seems a far-away cry from the subject in hand ; this 
is what he observes : Carefully comparing observations of forty 
immersions and emersions of the satellites, he finds that there 
is a variation in the moments of their reappearance of some 
seconds, depending on the time of the year. It is slight, but 
of the fact there can be no doubt ; how can it be explained ? 
The times of revolution ought to be absolutely equal. There 
seems no reason to suppose that the orbital time of the satellites 
varies ; they should be eclipsed and reappear with the punctu- 
ality of a clock. Can it be explained by the varying distance 
of the earth ? 

On the new estimates made by Cassini. when our globe is 



THE PROOF OF THE EARTH'S MOTION 285 

in opposition to Jupiter it is about a hundred and eighty million 
miles farther away than when it is in conjunction. If the trans- 
mission of light is not instantaneous, then the discrepancy in 
the observed times of the occultation will represent the time 
it takes light to cross the diameter of the earth's orbit. This 
Roemer estimated at twenty-two minutes. The speed of light, 
then, will be one hundred and eighty million miles divided by 
twenty-two minutes — that is, about eight million miles per 
minute. This is Roemer's explanation ; he presents it in a 
paper to the French Academy in November 1675. 

The history of science is full of fatuities. Roemer's dis- 
covery was laughed at by some, mostly ignored by others. 
Perhaps there was some reason. A few years later in the 
Principia, the disturbing influence of the planets and satellites 
one upon the other was disclosed. Newton records that the 
chapter on the inequalities of lunar motion cost him more 
labour than all the rest of the book. Jupiter had then four 
known sateUites ; they mutually pull each other about. Their 
motions represent one of the most difficult problems in astro- 
nomy. This might explain the inequality in the duration of 
their eclipses. 

Then, too, a speed of a hundred thousand miles or more 
per second was something too vast for the mind easily to grasp. 
Such a speed did not, however, appear absurd to Newton, for 
at least in the second edition of his Optiks he utilised 
Roemer's method, and calculated the time for the light of the 
sun to reach the earth at seven and a half minutes. This was 
an error only of a little more than half a minute ; but the close 
approximation was an accident ; he set the sun at only seventy 
million miles away. Yet even so great an authority could not 
induce general acceptance of Roemer's theory. It was another 
observer, travelling a widely different path, who was to confirm 
his results in a singular way. 

As far back as 1667 Picard, the French astronomer whose 
measures of the earth were to confirm Newton's discovery of 
the law of attraction, had observed a periodical movement of 
the pole-star to the extent of about 20". This, he saw, could 
neither be the effect of parallax nor of refraction ; it was 
very regular, and extreme at opposite seasons of the year. He 
could not divine the cause, neither could his young protege 



286 THE WORLD MACHINE 

Roemer. Not even after Roemer had worked out the velocity 
of light did the cause of this wandering occur to him ; not to 
him nor to any one else for half a century. 

Fifteen years after Roemer's death, two years before that 
of Newton, Samuel Molyneux, a wealthy amateur, had set up 
at Kew a magnificent sextant of twenty-four feet radius. His 
intent was to confirm or disprove the parallax of some of the 
fixed stars which Hooke had claimed he had observed. He 
associated with him the young Savilian Professor of Astronomy 
at Oxford, James Bradley. A little later, Molyneux gave up 
the work for other duties, and Bradley went on alone. Their 
idea had been to take a single star, watch it very closely from 
one season to the other, that is to say, from one side of the 
sun and the other, thinking that by means of their new instru- 
ment the question could be settled. 

What they were in search of was some shift in the relative 
position of two stars very close to each other ; such a shift as 
one might observe in the relative position of two peaks or two 
church spires seen from two distantly separated points. What 
Bradley found was an odd shift in the position of the star itself. 
He had made the same observation as had Picard, but on 
another star. It was not in the least what he was looking for, 
but it was certainly something new, and he followed up his 
observation with others through three or four years. Wherever 
he turned his instrument the disclosure was the same, with this 
difference, that whereas some of the stars seemed to describe 
a little ellipse, others would wobble in longer and longer ellipses, 
until it amounted simply to a movement back and forth along 
a straight line. 

The movement was extremely small, only about 20" at the 
most ; that is, a little more than the hundredth part of the 
apparent diameter of the sun and moon. But it was there ; 
moreover it was universal. So far from being fixed, the whole 
firmament was in a wobble — very minute, indeed, but neverthe- 
less measurable. What was the explanation ? Obviously, until 
the matter could be cleared up, pt was no use to think of 
measuring parallax. 

As the story runs, the explanation came to Bradley one day 
in a boat on the Thames. Whenever the course of the boat was 
changed, the apparent direction of the wind changed with it. 
It flashed across the astronomer's mind that the position of an 



THE PROOF OF THE EARTH'S MOTION 287 

observer on the earth is just the same as that of a man sailing 
in a boat ; and if light, like the wind, has a measurable speed, 
as Roemer and Newton supposed, then obviously the apparent 
direction of the stars would be an effect compounded of the 
double movement of the earth and the light. 

Up to that time observers had been going upon the theory 
that the flash of light from the stars is instantaneous — therefore, 
that the motion of the earth need not be taken into considera- 
tion. To them the problem in fixing the location of the star 
was much the same as that of the professor of mechanics in 
a familiar tale, through whose window one night a bullet came 
crashing from across the green. By observing carefully the hole 
in the window and in the wall opposite, and calculating the 
path of the projectile, it was an easy matter for a mathematician 
to determine from which student's room the careless shot had 
come. 

But suppose that the observer is aboard a vessel flying along 
at tremendous speed ; then, in calculating the point from which 
the shot is fired, the speed of the vessel must be taken into 
consideration. If its speed be great enough, the hole in the 
wall opposite the window will lag a little behind the point where 
the bullet would have struck had the vessel been standing still. 
Obviously the lag will be greatest when the shot is fired directly 
at right angles to the path of the ship's motion ; it will grow 
less the nearer the path of the projectile agrees with the path 
of the ship, and disappear entirely when the agreement is 
complete. 

All this is precisely what Bradley observed. If the effect 
he had detected is due to the finite speed of light, then it was 
not difficult to calculate from his measurements that the velocity 
of light must be very close to ten thousand times the speed of 
the earth. The earth shoots along its track at nineteen miles 
per second ; ten thousand times that is one hundred and ninety 
thousand. The figure was considerably higher than Roemer 's, 
very close to Newton's. There could no longer be any doubt 
that the speed of light is finite, and that its measure was known. 
It is to be noted that Roemer had computed the velocity of 
reflected solar light, Bradley the direct light of the stars. For 
a time it was supposed that the discrepancy might be in this 
difference ; but from the discussion of a thousand eclipses of 
Jupiter's satellites, instead of the forty which Roemer could 



288 THE WORLD MACHINE 

utilise, Delambre found that the agreement with Bradley's esti- 
mates is very close. Other measures have confirmed the result, 
correcting it a very little. It is now possible to effect the 
measure by mechanical means — with revolving mirrors, for ex- 
ample — along something of the same lines as the futile experi- 
ment of Gahleo. 

Bradley's discovery was a great step forward. It added a 
new and undreamt-of accuracy to astronomical observations ; 
it proved a great impetus in the study of optical phenomena of 
light. But it had a further and distinctly greater import : it 
demonstrated unequivocally the motion of the earth. The aberra- 
tion of the stars could be explained upon no other supposition. 
The accuracy of the observations was unquestionable. It was 
inconceivable that one section of the heavens should show this 
foolish little wobble while another section did not, on the sup- 
position that the earth was the fixed centre of the universe. 

It was given to Bradley to make yet another noteworthy dis- 
covery. That was the nutation or nodding of the earth's axis. 
Coppernicus, it wiU be remembered, had pointed out a conical 
movement of the earth's axis, extending through a period of about 
twenty-six thousand years. Newton had given the explanation 
of this movement in the Principia. Bradley discovered a dis- 
placement of some of the stars which could be explained neither 
from this motion of precession nor of aberration. He must have 
been a tenacious, patient sort of a man, for he watched the 
displacement through a period of nineteen years, and thus found 
it to be periodic. Of course, this could not be a movement 
of the stars themselves. His discovery was that, superimposed 
upon the conical motion was a secondary motion or inchnation ; 
it caused the line marked out by the extension of the earth's 
axis upon the heavens to pursue a wavy and scollopy sort oi 
motion instead of being a perfect circle. This motion, hke the 
other, is the result of the varying pull of the moon upon the 
oblate spheroid of the earth. It was predictable from Newton's 
theory ; he even suggested that it might exist, though it was 
a solar rather than a lunar disturbance which he had in mind. 

These discoveries of Bradley were, as we see, made quite 
by the way. What he set out for he never found. Not even 
with his wonderful zenith sextant, which could enable him to 
plot stellar changes whose maximum was but 20" of arc. 



THE PROOF OF THE EARTH'S MOTION 289 

could he detect any shift of position which he could regard as 
certainly due to stellar parallax. His discovery of the cause 
of aberration was announced in 1729. They did him due 
honour, and made him Astronomer Royal. There, by the 
minute precision and wide range of his observations, he laid the 
foundations from which in after centuries the theory of the 
universe will be builded, and of which some beginnings have 
been made in our own time. He was the founder of modern 
stellar astronomy ; but it was not until a century after him 
that the invention of the heliometer made possible the dis- 
covery which had been the real quest of his quiet, fruitful life. 

Meantime there were problems of nearer import to dwellers 
within our little solar world. 



CHAPTER XXIII 

LAPLACE AND THE STABILITY OF THE 
SOLAR SYSTEM 



Physico-mechanical laws are, as it were, the telescope of our 
spiritual eye, which can penetrate into the deepest night of times 
past and. to come. 

Helmholtz, On the Interaction of Natural Forces. 



CHAPTER XXIII 

LAPLACE AND THE STABILITY OF THE 
SOLAR SYSTEM 

In the history of intellectual development, more especially in 
the development of science, precedence among the nations 
seems to flit about in a lawless way. In the workaday world 
in which we live, one of the strongest forces is that of heredity ; 
its workings are revealed not merely among families, but in 
the larger forms which we may call social, the inheritance from 
one generation to another of ideas, customs, beliefs. The fact 
is one of the foundation-stones of the growing science of 
sociology. 

But genius for discovery, for invention, for the grouping 
and generalisation of phenomena into broad and simple laws, 
seems to escape the force of heredity entirely. One would 
readily think that the career of a great man would mean the 
impregnation of a generation and a people with his ways of 
thinking and ways of doing, and that when he had gone there 
would arise a distinct progeny to carry on his work. But it 
does not seem to be so. Poland did not become the leader 
of the intellectual world because of Coppernicus, nor Germany 
because of Kepler, nor Italy because of Galileo. Newton had 
no successors among his own people nor in the generation that 
followed. It was the mathematicians of France who were des- 
tined in the obscure order of events to take up his work. 

There remained when he died a number of minor but none 
the less important problems ; subsequent facts, as they came 
to light, suggested several more. There was one of extreme 
intricacy which Newton may have pondered but which he never 
ventured to solve. 

The slow sway of the earth's axis, pointed out by Coppernicus 

and explained by Newton, was clearly a periodical disturbance. 

So was the secondary nodding or nutation of the axis discovered 

by Bradley. Their effects might be momentous — they might 

293 



294 THE WORLD MACHINE 

determine changes of climate, for example — and so men came 
afterwards to perceive. But they were not permanent. It was 
clear that some time or other the earth would return to pre- 
cisely the same conditions as that which had once prevailed ; 
it was merely making a round. 

But the fact that there could be any such deviation from 
seeming regularity must have very soon suggested that there 
might be other changes whose effect was progressive and 
cumulative. Men came to wonder whether the seeming per- 
manent arrangement of the planets formed a stable system, or 
whether it might one day go all awry. Has this little patch 
of the universe which we call the solar system always existed 
more or less in its present form ? Were the planets always 
arranged in the same order and same distance and with the 
same speeds as we perceive them now, or is there underneath 
all this apparent regularity, this machine-like motion, a subtle 
deviation which in the course of uncounted ages will change 
it utterly. 

There was a curious fact turned up by Halley. Studying 
the records of some of the old eclipses, he found that the cal- 
culation, so far as he could perceive, of the times in which they 
should have occurred did not agree with the records at all. 
In the pages of Ptolemy and others he found accurate descrip- 
tions of eclipses which had taken place far back in the old 
Babylonian and Chaldean days. They did not tally with his 
computations by nearly two hours. This in a period of twenty- 
four hundred years is not a great variation ; there was always 
a chance, of course, that his calculations, or the ideas upon 
which he based them, were wrong. But the new methods 
brought in by Newton had reduced planetary motion to a 
science of marvellous accuracy. So, when the estimates had 
been carefully checked up and found flawless, astronomers were 
able to lay hold of any such discrepancy as a distinct and signifi- 
cant fact ; they could go hunting for the reason, rather than 
put the matter aside as something inexplicable or the mere 
product of error. 

Halley did not find the solution of the problem he had posed. 
Before it could come it was needful to clear up a difficult and 
highly recondite problem, the pull of the planets on each other, 
their mutual perturbations, as it is known — in more technical 
phrase, the problem of three bodies. For this, in turn, mathe- 



THE STABILITY OF THE SOLAR SYSTEM 295 

matical analysis had to grow to new powers. Newton had 
lent a powerful aid with his invention of fluxions. The philo- 
sopher Leibnitz had made very near the same discovery. To- 
gether they had produced the new calculus. It was the new 
weapon of analysis which, when the " Mathematical Principles/' 
the Principia, finally had taken hold, gave such a tremendous 
impetus to the mathematical treatment of scientific problems, 
and especially those of astronomy. There seemed to spring up 
a whole school of calculating geniuses to whom an unsolved 
problem was as meat and drink. 

The foremost of the earlier ones was Euler, a Swiss. It is 
related of him that when in middle life he lost one of his eyes, 
he remarked that henceforth he would have less to distract him 
from mathematics. Later on he lost the use of the other ; but 
it seemed to make no difference in his astonishing activity. 
Princes of the mind were then high in the favour of princes of 
the land. Euler roamed about the courts of Europe, joining 
first in the organisation of the newly created Academy of Sciences 
in St. Petersburg, then in Frederick's reorganisation of the 
Academy at Berlin, then back again. All the while he was turn- 
ing out with an incredible rapidity papers upon new methods of 
analysis, abstract dynamics, optics, the motion of fluids, the 
movement of the planets ; every branch of physical investigation 
seemed grist for his mill. Altogether he left some eight hundred 
memoirs, besides several respectable volumes, and a charming 
series of letters on the study of nature, addressed to a princess 
friend. His versatility was amazing. It may be noted in passing 
that this seems a characteristic of minds of the highest order. 
It was particularly true in the first two centuries after Galileo, 
before the sciences had become so intricate and highly special- 
ised that mastery in more than one narrow field should make 
a Helmholtz a marvel to his kind. 

Euler's association with the Bernouillis was so close that he 
might almost be regarded as a member of that famous family 
of mathematicians, two of whom were rivals of Newton, and 
one of whom, Daniel Bernouilli, was the first important 
Newtonian among mathematicians outside of Great Britain. 
Euler and the latter found a keen competitor in the precocious 
genius of Clairaut. He is remembered now, if he is remembered 
at all, chiefly for his classical investigations into the figure of 
the earth ; but in his own time his celebrity was considerable. 



296 THE WORLD MACHINE 

He had the gift of great personal charm ; he hked to use it, 
and he formed one of those distinguished and supple-minded 
figures which graced the salons of the period, and lent solidity 
as well as brilliancy to a mode of human congregation whose 
disappearance from present-day society, lovers of the varied 
life may scarce view without regret. 

Clairaut found a rival as aggressive as he was polished and 
suave in the foundling, Jean-le-Rond d'Alembert. Left as an 
infant on the steps of a church in Paris, and growing up to a 
gloomy view of the world, d'Alembert lives for us now chiefly 
as the collaborator, with Diderot and Voltaire, in the production 
of the famous Encyclopedie, and as the luckless victim of the 
versatile affections of another waif of fortune, Julie de I'Espinasse. 
He undoubtedly exercised a very considerable influence upon 
the political and philosophical thought of the time ; but he was 
primarily a mathematician, and worthy of rank with the highest. 

It was a rather curious coincidence that three of this group, 
Euler, Clairaut, and d'Alembert, all succeeded in obtaining in- 
dependently, and very nearly simultaneously, the solution of 
the problem of three bodies — the means of calculating the 
mutual share of three planets, for example, acting one upon 
another by the force of gravitation. 

They did not reach the larger problem : whether or no our 
system will endure. That was the work of their successors — in 
foremost line Lagrange and yet another mathematical genius 
whom the French are proud to class with Newton himself. This 
was that Baron Laplace who, through aU the stormy times of 
the downfall of the ancient regime, the Revolution, the Empire, 
the Restoration, managed to balance himself with such dexterity 
as always to keep a comfortable berth and retain the favour of 
the whilom reigning powers. 

Laplace had come up from the soil like all the rest ; he 
was merely a peasant lad in the fields of Normandy, the son of 
a poor farmer. Some of the neighbours, or perhaps the parish 
cure, discovered his amazing genius for calculation, and gave 
him a start. After that his own abilities, alike as a politician, 
which were unsurpassed, and as a mathematician, which were 
of the highest order, were sufficient. 

There is a story of how, at eighteen, he came up to Paris 
with a letter to the then reigning mathematician, d'Alembert, 



THE STABILITY OF THE SOLAR SYSTEM 297 

but gained no audience. Then he sent to the savant a letter 
on the principles of mechanics. It brought him a post at the 
military school, and a courtly word from d'Alembert that such 
a letter would be an introduction anywhere in Europe. There- 
with his successful way began. 

In taking up the " acceleration of the moon's mean motion," 
this steady shortening of the month which Halley had disclosed, 
Laplace was led to a still more important discovery ; that was 
the changing eccentricity of the earth's orbit. The elliptical 
form of the earth's path about the sun, he found, was steadily 
growing less and less. This was the cause of the quickening 
of the moon's motion. Laplace calculated it all out, figured 
that the real amount of quickening was ten seconds in a century 
— instead of twelve, as Halley had estimated — and that this 
was precisely what the theory of attraction required. 

But immediately came the question : How long had this 
decrease in the eccentricity of the earth's orbit been going on ? 
Was the eccentricity once immensely greater than it is now ; 
did the path of the earth once resemble that of a comet ; in 
times gone by, did it shoot down close to the sun into regions 
of blazing heat, then whirl about and rush away again into 
distant spaces of chilling cold, as the comets do ? It was a 
tremendously interesting problem, for it might give a clue to 
the whole past history of the earth — ^perhaps a hint as to its 
future as well. 

The memoir which Laplace at length presented to the French 
Academy dealing with this question was of profound philosophic 
significance. His answer was : The variation of eccentricity is 
not cumulative ; it is, like the precession of the equinoxes, like 
nutation, a periodic variation, requiring for its completion a 
long period of time. The latter Laplace estimated at eighty- 
six thousand years. It was a glowing triumph of the cal- 
culating faculty, and it was the foundation of a wonderful work. 
This was that great Mecanique Celeste — the Mechanics of the 
Heavens — to which Laplace owes, largely, his fame. Its central 
idea is the perfect balance revealed in every motion of the 
planetary system. It seemed to rule out all change as Newton 
had excluded chance ; it presented the solar machine as a vast 
engine, subject to slight variations in the motions of its parts, 
but whirling on without substantial deviations throughout in- 
finity. We now know that there was in Laplace's calculations 



298 THE WORLD MACHINE 

a seemingly infinitesimal error — that the solar system is not 
absolutely stable — and in our own day this has given us just 
that far glimpse backward which the results of the French 
mathematician seem to refuse. 

But in his own day theory and computation seemed to unite 
in exhibiting a celestial mechanism so perfect as to be self- 
sufficient. So Laplace regarded it. There had grown up in 
France in the eighteenth century a school of philosophers who 
had undertaken to explain the universe without the aid or 
intervention of the antique hypotheses as to the origin of the 
world. They had swept far beyond Voltaire. The apostle of 
Newtonianism in France is often thought of nowadays as a very 
godless man ; as a matter of fact he was a sincere deist, and 
even whilst he lived he had grown to the generation round him 
very much out of date. 

When the Scotch philosopher Hume visited France a little 
while before the outbreak of the Revolution, he chanced to 
remark one evening at dinner that he had never known an 
atheist — hinted even that he regarded such a class as a myth. 

" Monsieur," replied his host, the amiable Baron d'Holbach, 
" you are at table with seventeen." 

The ideas of Laplace partook of the spirit of the time. There 
is a famous old anecdote, oft repeated, of his encounter one day 
with Napoleon. Laplace seems to us at this distance very much 
of a time-server, very ready to crook the pregnant hinges ; he 
changed the dedication of his work from king to consul, from 
consul back again to king, as the times changed, with a com- 
placency that was admirably serene. But for once his courage, 
or his fondness for saying smart things, got the better of his 
smug compliance. As the anecdote goes, he had presented 
Napoleon with a copy of his latest work. The Corsican parvenu 
bore a deal of resemblance to the gallery-playing potentates of 
a later day, and loved, like these, to disclose the variety of 
his aptitudes and interests. He said to Laplace : 

*' Monsieur, I have examined your work, and I find therein 
no room for the existence of God." 

" Sire," replied Laplace, " I find no need for such an 
hypothesis." 

The work of Laplace was largely done in close association 
with another great French mathematician, a quiet and simple 



THE STABILITY OF THE SOLAR SYSTEM 299 

man, who lived chiefly upon nuts and fruits, planned methodi- 
cally each day what he should do the next, who cared nothing 
for place nor the glitter of the court like Laplace, who lived 
to calculate, to meditate, incidentally to render into very ad- 
mirable prose the famous poem. On Nature, of Lucretius. This 
was Lagrange. He was thirteen years the elder of Laplace, 
and is often thought to have been the more solid, as he was 
certainly the less showy man. 

It is an idle speculation ; both were men of prodigious power 
in analysis ; their peculiar abilities seemed to be a kind of com- 
plement one to the other. It was Lagrange who worked out 
the problem of the changing shape of the earth's orbit, dis- 
covered by Laplace. It was Lagrange who showed why it is 
that the moon turns towards us always the same face ; he 
figured out that the moon must bulge a little, just as the earth 
does, and that this would act as a sort of a brake on the revolution 
of the moon, so that it would eventually come to a standstill. 
It was Lagrange who worked out the general method connecting 
the rate of change in the variations of planetary orbits with the 
disturbing forces. But in general they worked so closely to- 
gether, the one taking up the problems of the other, and vice 
versa, that their names are usually linked in any account of the 
achievements of the period. 

This peculiar relationship was in no wise disturbed by the 
translation of Lagrange to Berlin in 1766. Students of the 
period — and it was a heyday time for philosophers and men 
of science in general — will recall that the fat Frederick, sur- 
named The Great, was then doing what he could to Parisianise 
the German capital. He had established an Academy like unto 
that which has rendered such signal services to France, and as 
there was a dearth at that time of native material, he imported 
half the great figures of France — Voltaire, Maupertuis, Lamettrie, 
d'Argens, and many another. 

There came a vacancy in the mathematical section. Frederick 
had a taste for fine phrases as well as an excellent opinion of him- 
self ; he even wrote verses, whose halting metre a wit of the 
time remarked would limp after him in history. In his invita- 
tion to Lagrange to come and fill the vacant post, he explained 
that the greatest king of Europe wished to have the greatest 
mathematician in Europe at his court. It was a fine place to 
go ; an invitation couched in such language was hardly to be 



300 THE WORLD MACHINE 

refused. Lagrange went, and there he remained for twenty- 
one years. It was at BerHn that he completed his great 
Mecanique Analytique, a superb work, practically the foundation 
of that especial science ; it would have given him an enviable 
fame had he done nothing more. 

These two giants, Laplace and Lagrange, so largely mono- 
polised the stage as to dwarf into a minor place an excellent 
mathematician, a dreaming genius, Johann Heinrich Lambert, 
tailor's apprentice of Miihlhausen, of whose majestic reveries 
we shaU hear hereafter. It was a discovery by Lambert — one 
that he did not live to solve himself — that gave to Laplace and 
Lagrange one of their most celebrated problems. 

HaUey, who pointed out so much for others to think about, 
had noted that the motion of Saturn was swifter than it ought 
to be, according to the Newtonian theory, while that of Jupiter 
was slower. Lambert found that Saturn in his day was moving 
faster than in Halley's time. There was evidently a fluctuation 
or disturbance of some sort at work. The situation was pretty 
obviously the result of the pull of one planet on the other, 
acting with or against the steady pull of the sun. But it was 
a mathematical puzzle of a very intricate order — the problem 
of three bodies over again. In many doubting, hesitating 
minds it was a stumbling-block to the acceptance of the theory 
of gravitation. In that day, just as in our own, there were, in 
abundance, types of minds which clung tenaciously to every- 
thing which seemed a difficulty or an obstacle in the path of 
any new idea. No doubt this type is of use, always ; it forms 
a kind of check upon over-enthusiastic spirits, refuses to accept 
any new result until it has been proven up to the hilt ; it is 
of undoubted value in sifting out fact from hasty theory, and 
in giving us a solid sense that what knowledge we may put by 
when the opposition has been cleared away is of real and lasting 
worth. 

The solution of the special case of Jupiter and Saturn proved 
a clue to other and less important planetary perturbations. It 
naturally was received with great acclaim by astronomers, 
since it seemed to sweep away the last hindrance to the full 
acceptance of the idea of attraction. This idea was no longer an 
hypothesis. After the demonstrations of Lagrange and Laplace, 
it would take rank as a theory beyond all cavil or doubt. Fifty 



THE STABILITY OF THE SOLAR SYSTEM 301 

years later, utilising these same methods, the theory was to 
receive at the hands of Leverrier and Adams a brilliant and 
clinching verification in the discovery of a new and unsuspected 
member of the solar system. 

This tacit partnership, undisturbed by the pitiful jealousies 
which disfigure so many pages of scientific history, closed with 
the death of Lagrange in 1813. He was almost wholly a mathe- 
matician. The range of Laplace was larger. He extended and, 
through wider applications, gave almost new life to the Theory 
of Chance — that is, the calculus of probabilities. He was asso- 
ciated with the chemist Lavoisier in many of the latter's in- 
vestigations. Together they produced an important memoir, 
which is one of the foundations of the modern theory of heat. 
Lagrange speculated little ; the mind of Laplace was sometimes 
given to wider flights. It was in one of these that he divined 
and sketched the grandiose conception which endeavours to 
account not merely for the present motions and actions, but 
the origin of worlds as well. He was not alone in working 
out this theory ; though he did not know it, he had a precursor 
in a near contemporary. Moreover, he threw it out as little 
more than a suggestion, at the close of the theoretical portion 
of his more popular Exposition du Systeme du Monde. The 
evidence which has given weight and prevalence to the Nebular 
Hypothesis has largely come since his day ; with it some diffi- 
culties which he could in no wise foresee. This, assuredly one 
of the profoundest flights of the human imagination, may well 
form matter of a later discussion. 

Thanks to Newton, we know what makes the world go. 
Thanks to Laplace, we know with precision how it goes. How 
large is this machine ? 



CHAPTER XXIV 

FIXING THE BOUNDARIES OF OUR SOLAR 
WORLD 



E pero, prima che tu piu t' inlei, 

Rimira in giuso, e vedi quanto mondo 
Sotto li piedi gia esser ti f ei ; 

Col viso ritornai per tutte quante 
Le sette spere, e vidi questo globo 

Tal, ch' io sorrisi del suo vil sembiante. 
E quel consiglio per miglior approbo 

Che r ha per meno ; e chi ad altro pensa, 
Chiamar si puote veramente probo. 

Vidi la figlia di Latona incensa 
Senza quell' ombra, che mi fu cagione 

Per che gia la credetta rara e densa. 
L' aspetto del tuo nato, Iperione, 

Quivi sostenni ; e vidi com' si muove 
Circa e vicino a lui Maia e Dione. 

Quindi m' apparve il temperar di Giove 
Tra '1 padre e '1 figlio ; e quindi mi fu chiaro 

II variar che fanno di lor dove : 
E tutti e sette mi si dimostraro 

Quanto son grandi, e quanto son veloci, 
E come sono in distante riparo. 

U aiuola, che fa tanto feroci, 
Volgendom'io con gli eterni GemelH, 

Tutta m' apparve da' colli alle foci. 

Paradiso, Canto xxii., 127. 



CHAPTER XXIV 

FIXING THE BOUNDARIES OF OUR SOLAR 
WORLD 

By an instinct inborn to the mind, man is for ever seeking 
limits and confines. The progress of astronomy brought a 
natural desire to know the shape and the dimensions of the 
planetary system to which we belong. Is Saturn at the edge ? 
Out beyond it. amid the seeming chaos of the stars, are there 
other " wanderers," turning and turning, like our own, about 
the sun, but in the distance lost to view ? For more than a 
century and a half the telescope added no new planet. Their 
number remained at that which had been known to the ancients. 
The optic tube had almost infinitely broadened man's ideas of 
the extent of the system itself, and of the stars beyond ; yet 
Saturn remained to Newton, as it was perhaps to the Chaldeans, 
the outer rim. 

In 1781 the news slipped across Europe that the Hmits of 
the solar system had suddenly been doubled. An obscure 
musician of Bath, in England, turned amateur astronomer, was 
sweeping the heavens with a small telescope, and was struck 
by a curious appearance in the constellation of the Twins. It 
was very much larger than any of the surrounding stars ; he 
therefore suspected it to be a comet, and the attention of astro- 
nomers was drawn thereto. The close study of the comets was 
in the order of the day ; many attempts were made to compute 
its path. At last it became clear that it was no comet, but that 
it moved in a circle, nearly. It was a new planet, revolving 
about the sun at a distance of close to twenty times that of the 
earth. 

The discovery made a tremendous sensation, and it made 
fame for the man whose view had held it first. For our earthly 
concerns the later event was undoubtedly of more importance 
than the discovery itself. It was not a wonderful discovery, 
either in the instruments employed or in the sense of having 

30s u 



3o6 THE WORLD MACHINE 

been predicted and calculated as the consequence of some law, 
or a long series of observations. It was purely an accident, 
made, moreover, by means of a relatively small telescope. It 
undoubtedly would have been made by some other observer, 
probably within a few years, since star maps were coming into 
fashion more and more ; the changing position of the planet 
must have soon been noted. 

But what the discovery did was to lift from poverty and 
obscurity one of the most wonderful observing geniuses known 
in the history of astronomy. This was Herschel ; his larger 
deeds were in the realms of stellar research, and they will fill 
a sequent chapter. Simple and loyal subject that he was, 
Herschel claimed the right of discovery, and wished to name the 
planet after his king, George III. The continentals did not 
take to the suggestion ; some of them wished to name it after 
Herschel himself, and so for a time it was known. Finally 
it was agreed to draw a name from the ancient myths, like 
those of the other planets, and deeming that Uranus may have 
been the earliest of the astronomers, it perpetuates his twilight 
fame. 

The new planet was in no wise remarkable, save as to its 
distance. It was only about half the diameter of its neighbour 
Saturn, though seventy or eighty times the volume of our pigmy 
earth. One peculiarity of its distance was promptly noted ; 
just as with most of the planets, its orbit lay at about twice the 
distance from the sun as that of its next nearest neighbour. 
Saturn is at ten times the distance of the earth ; Uranus was 
found to be very closely twenty times. Promptly the astrono- 
mers began to search for yet further outlying members of the 
system. 

The probable existence of at least one more planet was borne 
in by the curious discrepancies observed in the orbit of Uranus. 
The discovery of this conjectured planet was one of the greatest 
triumphs, though not the final, of Newton's ideas. Before it 
could be made there was another, or rather a series, of not 
less interest. 

Even in the solar system as it was known before Herschel, 
there was a curious gap. If the distance of Mercury from the 
sun be taken as unity, it was noted that Venus was very nearly 
twice this distance, and that each successive planet was some- 
thing like double that of the next. The relationship is not 



BOUNDARIES OF OUR SOLAR WORLD 307 

exact ; the distance grows less and less as you journey outwards. 
Thus, the earth is only two and a half times the distance of 
Mercury ; Mars is only about one and a half times the distance 
of the earth. But Jupiter is five times. Between Mars and the 
great planet there is a broad space that, even for HerscheFs 
wonderful telescopes, seemed empty. Kepler had speculated 
upon this gap, had dreamed of a missing planet. There was no 
mistaking the fact that there was some sort of order in the 
distribution of distances. Saturn was very closely twice the 
distance of Jupiter. All sorts of ratios were tried in the en- 
deavour to find an exact law. 

Finally, taking a hint from Titius, in 1772 the astronomer 
Bode of BerHn noted that if by taking a little different geomet- 
rical progression than that of simple doubling, and by adding 
a constant each time, a very close approximation could be 
found. Thus, if the series be taken as o, 3, 6, 12, 24, and so 
on, and the number 4 be added at each step, the result is a 
series which expresses fairly well the relative distances. This 
is what is known as Bode's law. The discovery of Uranus, 
twice the distance of Saturn, a short time after, seemed to 
indicate that it was a veritable law. It deepened the mystery 
of the extra-Martian gap. 

The upshot of it was that a little committee of astronomers 
was formed to search for Kepler's hypothetical planet. The 
zodiac and its adjacent regions was divided into twenty-four 
parts ; each was portioned off to an observer. Undoubtedly 
the discovery that followed would have been made very shortly ; 
as a matter of fact, it was an accident. Quite unknown to 
this special committee, Piazzi in Sicily, engaged in making a 
catalogue of the stars, noted one evening a small object which 
had no place on his map. It was the first night of the nine- 
teenth century. The next evening it had shifted a little ; so 
on through a fortnight or more, until he was convinced that 
it could not be a star. Like Herschel with Uranus, he thought 
it might be a comet. It was quite invisible to the eye ; if 
it were a star it could not be above the eighth magnitude. In 
his puzzlement he wrote to two of his friends ; one of these 
was Bode. 

The supreme test of any natural law is the element of pre- 
dictability. If after some striking relationship, some succession 
in the order of events, some apparently methodical arrangement, 



3o8 THE WORLD MACHINE 

has been observed, new facts come to light, our instant question 
is : Do fact and theory hang together ? If not, then, as it were, 
the theory hangs alone. But if they do — ^if, moreover, the 
new facts be such that they might have been more or less cal- 
culated or divined from the previous arrangement — ^we have a 
feeling of certitude which nothing else can bring. When Bode 
opened Piazzi's letter his mind instantly leaped to the idea 
that here was the missing link of his system. 

But by that time the object, whatever it was, had disap- 
peared from view ; he could not find it. Could its position be 
calculated ? Mathematicians tried hard ; but the observations 
which Piazzi had been able to make were few in number, and 
very close one to the other. The difficulty resulted in the dis- 
covery of a mathematician of the first order, one of the greatest 
since Laplace. 

There was at that time in Germany a young private tutor 
who had invented several new methods of analysis, among 
others that which now bears the name of the " method of least 
squares." By the aid of the latter he was able not merely to 
construct the orbit of the new planet, for such he found it to 
be, but to indicate to the astronomers the point where later 
on it would be found. Just a year after Piazzi first had sight 
of it, it was sighted again, close by where the young Gauss 
had predicted. It was Piazzi's obvious right to name it, and 
he called it after Sicily's protecting goddess, Ceres. 

What Bode had surmised turned out to be true ; it lay 
between Mars and Jupiter. As calculated by Gauss, its dis- 
tance from the sun was 2.7 times that of the earth. In the 
system of Bode it should have been 2.8. The agreement was 
remarkable, but the planet was disappointing. As best it was 
clearly only a few hundred miles in diameter ; it was smaller 
than any heavenly body known at that time. It revolved like 
the other planets ; but its orbit was extremely eccentric, and 
it was tipped up ten degrees to the ecliptic, a greater amount 
than that of any other planet then known. Altogether it was 
a puzzle. 

The puzzle deepened when, a few months after, another 
German astronomer, Olbers, found a second. Gauss again cal- 
culated its path. It was found to be at almost the same distance 
from the sun as Ceres, revolving in a yet more eccentric orbit 
and tilted to the ecliptic at thirty-four degrees. Its bulk was 



BOUNDARIES OF OUR SOLAR WORLD 309 

about the same as Ceres. Here was a mystery. Two planets, 
evidently true planets, had been found ; but they were more 
Hke fragments than the respectable bodies they should have 
been. The fact that their orbits were so close to each other — 
roughly speaking, identical — heightened the impression. It was 
surmised by Olbers that they were in reality bits of a larger 
planet, and he set about a systematic search for the missing 
pieces. 

Seven years of patient observation brought from the depths 
a third. Again the observations were turned over to Gauss, to 
map its path in space. It closely resembled the others. To 
the second he had given the name of Pallas ; the third he 
called Vesta. It was as absurdly small as the others. It is just 
visible to the unaided eye. Olbers kept up his hunt for other 
fragments, as he deemed them, for thirty years more : he had 
no further reward. Soon after he died a fourth was found ; 
then a fifth ; then they came tumbling in so fast that it takes 
a long catalogue to number them. Up to the present time 
near five hundred have been found. 

The largest was the third in order of discovery — Vesta. We 
now know that it is about five hundred miles in diameter. They 
range from that down to ten or twenty. But still they remain 
a puzzle. Even five hundred of them tossed together into a 
mould would not make a planet very much larger than the 
moon. Leverrier calculated from the observed disturbances in 
the orbital course of Mars that their combined pull was not 
equal to that of a planet one-quarter as large as the earth : 
it is known now that it is a great deal less. What is the 
explanation ? 

We do not know, for we have not as yet a theory of planet- 
ary evolution sufficiently complete to give a satisfactory account 
of this flying swarm. The idea of a " shattered planet " is 
attractive ; it was the most obvious, and it was the first that 
was suggested. It is conceivable that a planet might go to 
pieces in a terrific explosion. The craters of volcanoes long 
ago revealed to man the fact that the earth has a molten in- 
terior. Doubtless this is true of all planets. Veritable ex- 
plosions like that of Krakatoa a few years ago, are sufficient 
indication of the violence with which such a cataclysm might 
take place. If it ever did, the disrupted fragments would tend 
to go on circling the sun in something of the same sort of orbit. 



310 THE WORLD MACHINE 

And this is a good deal the appearance which the asteroids, as 
Herschel named them, present. 

The evidence in favour of this theory would be a great deal 
stronger if it were found that the asteroids pass successively 
through some common point in their closely associated orbits ; 
but that is what they do not seem to do. The zone in which 
they swing, this cinder-path of the solar system, is as broad 
as the distance from the earth to the sun ; their orbits are 
tilted to the ecliptic at all sorts of angles ; they are the most 
eccentric of planetary bodies. One of them comes nearer to 
the earth at times than any other body but the moon. 

It seems hkely that there was no " shattered planet," and 
that these small shot of the system are more probably a kind 
of sputter in the moulding of our solar world. If our system 
was formed through the coalescence of a succession of rings 
like those of Saturn, sloughed off successively from a great 
revolving pre-solar nebula, the formation of the vast mass of 
Jupiter might explain the asteroids. Its enormous bulk would 
exercise a disrupting influence, perhaps, upon a neighbouring 
planetary foetus, if we may conceive that such ever existed, 
and little by little what might have grown into an adult planet 
was pulled apart to form a crowd of dwarfs. 

However this may be, the Keplerian gap was in a measure 
filled ; the law of Bode seemed established. There did seem a 
discernible order in the arrangement of the planets. The new 
evidence in its favour was hardly more than presented than yet 
another discovery came which brought more of difficulty than 
the previous one had brought of aid. 

Interesting and even exciting as was the discovery of the first 
new planet, that of Uranus, it none the less brought trouble. 
For a time it seemed as if it could not be brought into agree- 
ment with the hard-won laws of planetary motion. It was very 
soon found that the planet had evidently been observed, though 
not recognised, nearly a century before ; the more carefully 
its motions were followed, and plotted, the more clear did it 
become that it did not fit with exactitude into the Keplerian- 
Newtonian scheme. The types of minds which discover a curious 
delight whenever the marching intellect of the race strikes a 
stumbling-block were offered a temporary joy. Perhaps the 
laws of gravitation were not universally true, and there might 
stiU be room in the world for that hodge-podge caprice which 



BOUNDARIES OF OUR SOLAR WORLD 311 

had been the essence of the old order of thought. Not 
long. 

As the wobbHng path of the tipsy planet became more and 
more accentuated, here and there were found minds to throw 
out a suggestion that the distortions indicated an extra-Uranian 
body. It was the most obvious explanation, and it presented 
a beautiful problem. The five or six heavy volumes of the 
Mecanique Celeste in which Laplace had embalmed the solar 
system in unchanging stability, were filled with the reverse 
problem here presented : his task had been to measure the mass 
of the component members, determine what disturbance each of 
them would exercise upon the other, then to find if observation 
agreed with the result. It was by this means that he detected 
the changing eccentricity of the orbit of the earth. Here the 
matter was : given a carefully observed disturbance, what and 
where is the planet, or the planets which cause it ? 

By 1840 the materials were sufficient. Some observers had 
already thought of a search, in a purely empirical way, for the 
disturbers. Meanwhile the problem had been independently 
attacked by two young mathematicians. One was an under- 
graduate at Cambridge University in England, John Couch 
Adams ; the other was Urbain Leverrier, in France, friend of 
the fiery and stimulating Arago. By October 1845, Adams had 
worked out his results and announced them in a letter to the 
English Astronomer Royal. The actions of Uranus could be 
explained by assuming an outer planet which, according to 
his reckoning, was then moving along at such and such a point 
in the heavens. So important a post as that of Astronomer 
Royal must, to be sure, be filled by a personage of distinction. 
This has its disadvantages. It was Huxley who remarked that 
the moment a man acquires a great reputation in science 
he becomes a nuisance. The remark found here an exempli- 
fication. 

If the Astronomer Royal had pointed his telescope towards 
the spot indicated by Adams he would have found the new 
planet within less than a couple of degrees of its calculated 
location. Instead of that he wrote back a letter with some 
foolish, vapid questions, quite in the spirit and quite on the 
customary mental level of official science and official investi- 
gation of any character whatever. Meanwhile Leverrier was 
ready with his results ; they were published in June 1846. The 



312 THE WORLD MACHINE 

distinguished Astronomer Royal received a copy of this paper 
as well ; he was astonished to find that the theoretical place 
of the planet, as calculated by the French mathematician, was 
within a degree of the point fixed by Adams. It is amazing 
to think that he could not be stirred to turn his telescope around 
and hunt, instead of writing another letter with the same ques- 
tions. But another letter he wrote. Adams meanwhile had 
been perfecting his calculations ; finally, the big telescope at 
Cambridge was brought into action. It must likewise have 
been in charge of a fat-wit, for the new planet was actually 
seen but not recognised ; his method, Newcomb says, was 
like that of a man who, knowing that a diamond had been 
dropped near a certain spot on the sea-beach, should remove 
all the sand in the neighbourhood to a convenient place where 
he might sift it at his leisure. 

No doubt others had tried ; it was a difficult quest. But 
in methodical, painstaking Germany they were making splendid 
star-maps. To the head of the Berlin Observatory Leverrier 
wrote a careful letter, fixing with very confident precision the 
point where the new planet could be found. The head of the 
institution, Galle, received the letter on an afternoon ; that 
night he swung his telescope round and the discovery was made. 
The planet was found exactly where these two mathematicians 
had reckoned it should be. In neither of the countries to which 
they belonged could the astronomers in charge of the great 
telescopes be roused to give heed to these unhonoured prophets. 
Thankfully there are not many similar instances in the history 
of the science, in which such extremes of brilliant investigation 
and ofiicial stupidity have come together with such luckless 
result. 

It was assuredly an amazing result, one of the spec- 
tacular triumphs of the calculating mind. There is scarce need 
to add that when it had come there could no longer be any 
doubt as to the universal application of Newton's law. By the 
aid of that law the hand of the astronomer had dipped into the 
distant waters of space and brought from its invisible depths 
a new world. Even while they hovered on the edge of the dis- 
covery. Sir John Herschel, in an address before the British 
Association, had very beautifully observed : — 

" The past year has given to us a new asteroid ; it has done 
more — it has given us the prospect of another planet. We see 



BOUNDARIES OF OUR SOLAR WORLD 313 

it as Columbus saw America from the shores of Spain. Its 
movements have been felt, trembling along the far-reaching line 
of our analysis with a certainty hardly inferior to ocular de- 
monstration." 

The discovery is often cited as one of the great feats of 
calculation ; it was hardly less a witness to the marvellous 
accuracy which astronomy had attained. The deviation of 
Uranus from its appointed path, set by Kepler's law, never ex- 
ceeded two astronomical minutes — that is, the thirtieth part of a 
degree. It lies just on the fringe of visibility ; Neptune far 
beyond. The one would probably never have been recognised 
as a planet but for the invention of the telescope ; without 
its present-day perfection, the second would never have been 
known. 

The last of the planets possessed, hke its immediate fore- 
runner, but few conspicuous traits. It is a little larger than 
Uranus ; like the latter, it rotates in an opposite direction to 
that of all the other planets. But its distance was a complete 
anomaly. If the law of Bode held good, it would have been 
found at something like twice the distance of Neptune — that 
is, at nearly forty times the distance of the earth from the sun. 
Instead of that, it is something less than thirty times. It had 
been difficult enough before to reconcile the observed distances 
of the planets with any absolute order of arrangement. With 
the discovery of Neptune's orbit, the idea of a simple " law " 
of distance was given up. Until we know more of planetary 
evolution than we do, it will be quite impossible to say why 
it is that the planets are spaced as they are. 

It remained a natural question as to whether the new planet 
was in reality the outermost member of the system, or whether 
others lay yet beyond. Sixty years and more of observation, 
scrupulous in its method, and with an ever-increasing delicacy 
of observing instruments, has failed to present even a suspicion 
of an ultra-Neptune. The orbit of the new planet showed no 
such wobbling as that which, in the motion of Uranus, had 
pointed to the existence of the other. We may conclude, there- 
fore, not absolutely, but with a considerable degree of pro- 
bability, that we now know the shape and size of our planetary 
world, and practically aU that is worth knowing of its contents. 

Our planetary system consists, then, of eight large bodies, 



314 THE WORLD MACHINE 

circled by twenty odd moons or satellites ; of a swarm of asteroids ; 
a number of more or less prominent comets. These revolve 
within a very thin, very broad zone, that we might picture 
as like a cart-wheel cheese, or a very thin grindstone ; or if you 
like, a very thick penny. In order of size or arrangement there 
seems no fixed relation ; the mass of a single planet is greater 
than that of all the rest of the satellites of the sun put together. 
Yet even with Jupiter added, they form but an infinitesimal 
portion of the sun itself — grains of small shot beside a cannon- 
ball. 

What lies beyond ? The answer, so far as we may gather, 
is simply : space — space and space, and, for all we shaU ever care, 
never an end. Neptune is distant from us thirty times farther 
than we are distant from the sun ; so far as we know, for a 
thousand times this distance there is nothing, save, it may be, 
swarms of meteorites, speeding comets, and fragments of ex- 
ploded worlds. There is certainly no star, no sun, within this 
distance ; if there were any dark body at all comparable with the 
grandeur of the sun, its existence would be disclosed by the 
disturbing influence it would exercise on the outer planets. 

Not in a thousand times the distance of Neptune, — not, in 
so far as we know, in nearly ten thousand times. Were we to 
picture the whole solar system as a huge vessel, perhaps the 
size of the Lusitania, anchored or slowly floating in the midst 
of the lone wastes of the Atlantic, unvisited and uncompanioned 
by any other craft, large or small, we should have some sense 
of our isolation in the cosmos. 

Are we anchored, or do we drift ? Our sun is obviously 
one of the stars. Is it, and are they, fixed and immutable within 
the eternity of space and time ? Was this universe of flaming 
suns cast, as it were, in a soHd mould ? If there be motion, 
do we merely drift, or are we speeding the stellar ways at 
velocities compared with which the flash of the cannon-ball 
would seem hke the leisurely meandering of a sluggish stream ? 
If we move, where, in distant aeons, shall we bring up ? 



CHAPTER XXV 

HERSCHEL AND THE HELTER-SKELTER FLIGHT 
OF THE STARS 



A moody child and wildly wise 

Pursued the game with joyful eyes 

Which chose, like meteors, their way, 

And rived the dark with private ray : 

They overleapt the horizon's edge. 

Searched with Apollo's privilege ; 

Through man, and woman, and sea, and star, 

Saw the dance of nature forward far ; 

Through worlds, and races, and terms and times, 

Saw musical order, and pairing rhymes. 

Emerson. 

How can Dryasdust interpret such things, the dark, chaotic 
dullard, who knows the meaning of nothing cosmic or noble, nor 
ever will know ? 

Carlyle, Sartor. 



CHAPTER XXV 

HERSCHEL AND THE HELTER-SKELTER FLIGHT 
OF THE STARS 

The surface velocity of the earth, especially between the tropics, 
is high — seventeen miles per minute, fifty times swifter than 
the swiftest cannon-ball. Seen from the centre of the earth, 
it would appear very slow ; the hands of a clock turn twenty- 
four times while the earth turns once. Relatively, a huge Ferris 
wheel, revolving once in a few minutes, goes hundreds of times 
as fast. The whole great earth booms through space at nearly 
sixty times the speed of its surface in revolution, nineteen miles 
per second, two thousand times the cannon-ball. Yet from the 
sun, this dizzy flight would be imperceptible save to repeated 
observation ; the earth would pass over only one degree of a 
circle in a day. We could think of it as fixed at the end 
of a spoke in a wheel ; the earth turns about this solar axis once 
in a year. 

For us the crystal sphere of the stars is a globe, our earth its 
centre. Does it too revolve ? Should we ever know if it did ? 

When measurements of the telescope had reached an accuracy 
of a second of arc and the stars revealed no parallax, it was 
clear they were beyond two hundred thousand times the distance 
of the sun. Conceive that they are all turning about our sun, 
hke the planets. The length, the circumference, of circles are 
to each other as their radii. If the stars moved as swiftly as 
the earth, then at this distance their " year " would be two 
hundred thousand of ours. They would require six hundred 
of our years to cover a degree. Their apparent annual motion 
then would be about six seconds of arc. 

No such motion as this could be perceived ; for a long time 
no motion at all. Yet, here and there, it did seem that, in 
very long periods, some of the stars had shifted place slightly. 

Early in the century Halley, the sower of much seed, the 

harvest from whigh others would reap, had pointed out that 

317 



3i8 THE WORLD MACHINE 

at least three of the best-known stars of the heavens, Sirius, 
Arcturus, and Procyon, had certainly changed in their incUna- 
tion to the ecliptic since Greek days, if the star maps of the 
Alexandrian astronomers could be relied upon. His view was 
strengthened by the fact that the brightest of all, the Dog- 
star, had perceptibly altered its position since the days of Tycho 
Brahe. Comparison of the ancient records of other stars in- 
dicated other probable deviations ; but the motion, the change, 
was so minute that it might readily be an illusion or an error. 

So far as the most careful observer gazing up at the sky 
could see, it has in no wise changed from the times of the 
earliest Greeks. Probably they had records now lost to us. 
Doubtless they made comparisons as did Halley, with all the 
care and accuracy at their command. Their idea was that the 
stars were fixed. So, for aught that the sceptic Halley could 
demonstrate, they remained. 

Then came Bradley's discoveries showing how a considerable 
degree of apparent motion could be accounted for, simply from 
the annual motion of the earth, and the swaying of its axis. 
When, half a century later, Herschel began his investigations, 
the question was still open. The proof that they do move 
and much more beside, was his. 

The attribute of genius is flung about rather carelessly at, 
times ; such a quality alone can account for such a career as 
that of this poor German musician, who became the greatest 
observing astronomer of his age. Kepler, we recall, came up 
from a pot-boy ; the origins of Galileo and Newton were quite 
as humble ; but all of them had a university career. Herschel 
had none. He was thirty-five before he had ever looked through 
a telescope. His father was an oboe player in a German 
regiment. It was not an intelHgent pursuit ; it is not ordinarily 
a stimulus to high deeds. The boy was brought up to the same 
task. His coming to England was through the removal of the 
Hanoverian guards to that country while he was playing in 
the regimental band. He was soon out of it ; shortly after- 
wards he becomes an organist and music teacher in Bath. So 
his life runs along tranquilly for ten or twelve years, years in 
which the bent of a man is usually revealed and developed. 
Herschel was studying ; the long day over, he was deep in mathe- 
matics, optics, languages, trying to make good the education 
which he had lacked. In the end he comes across a work in 



HELTER-SKELTER FLIGHT OF THE STARS 319 

astronomy. For the rest of his life in every spare moment he 
will think of nothing else. He determines to buy a telescope ; 
it is beyond his means ; he makes one of his own ; then another 
and another, until he has at last an excellent ten-foot reflector, 
and the real work of his life is begun. 

His industry must have been something prodigious. By 
day, in the intervals of teaching, he is grinding lenses for larger 
and larger telescopes. In the evenings he is conducting concerts 
and oratorios ; then sweeping the heavens for the rest of the 
night. He must have been of tough fibre to stand such a strain. 

After five or six years of it his reward comes. He discovers 
the comet-like star which turns out to be the new planet which 
they will call Uranus. In a spectacular way it is the biggest 
thing since the discovery of the telescope itself. Like Byron, 
he finds himself famous in a night. The Royal Society makes 
him a Fellow ; the King sends for him. He may now give 
up his concerts and music classes ; he has a workshop and an 
observatory of his own, with the princely salary of £200 a year. 
Astronomy becomes the fashionable fad of the time, and tele- 
scopes are in demand. He makes them by the score. But 
soon, from a friendly word, the King realises how absurd it is 
to have this wonderful man grinding lenses, and he is given 
money to build a great forty-foot instrument, which is the 
dearest dream of his days. It is a magnificent affair ; compare 
it for an instant with the resources of Galileo. His crude tubes 
would enlarge only thirty-two times, Herschel's several thou- 
sand — ^six thousand, one may read, but the figure is somewhat 
misleading. How the noble Florentine would have stared could 
he have seen it ; would he ever have left off observing if it could 
have been his ! 

But its creator is worthy of the instrument. What he did 
with it forms a good share of modern stellar astronomy. He 
maps and catalogues the stars, the nebulae as well. He dis- 
covers eight hundred double stars — stars which to the eye had 
seemed single. He passes in review the whole firmament open 
to his gaze, not a single time but four times, with a minute 
scrutiny as if he were searching for gold. He counts the number 
of stars in each of more than three thousand divisions which 
he makes of the firmament. 

From all this he rises to a yet greater discovery or, if any 
prefer, demonstration — that of the proper or straight-line motion 



320 THE WORLD MACHINE 

of the stars themselves. What many another astronomer, 
seeking as ardently as he, had failed to find, he made clear. 
Outside of any effect due to the refraction of the earth's atmos- 
phere, to the motion of the earth about the sun, to the aberra- 
tion of Hght, to the nodding of the earth's axis, he reveals, 
proves, that the stars move. Not to him will it be given to 
find their parallax, to compute their actual distance ; that must 
be the work of instruments yet more delicate than any he can 
contrive. But their relative motion at least he can disclose. 

It is no revolving heaven that he finds, no fixed order ; it 
seems aU a random, mindless, helter-skelter flight. A swarm 
of bees, a cloud of fire-flies, reveals as little purpose. Some- 
times it seems that there are real clusters ; almost aU of the 
Pleiades appear to move in a common direction — so do five of 
the seven stars of the Dipper. But, for the most part, it is 
chaotic enough ; side by side, one star is falling ever downwards, 
another rushing toward the zenith, two others speeding away 
in opposite level flight for the poles of the universe. Some may 
be describing orbits ; it seems fairly certain that others are 
not. Some are flashing across the abyss of space at such tre- 
mendous speed that the combined mass of a hundred million 
suns could not hold them in leash. 

Picturing it all, it seems like nothing so much as a wild dance, 
a mad Sir Roger de Coverley of suns, in a line that knows no 
end. Even now the mind cannot grasp it ; a poet perhaps, 
not we of common clay ! Yet, could our human kind wake 
to the full consciousness, the true significance, of this weird and 
seeming insensate riot of the stars, should it be happier, stronger, 
then than now ? 

''All a wonder and a wild surprise." And still, amid the 
confused movement of the heavens, there did seem, slowly 
emergent, one general fact. From it Herschel rises to that 
discovery of his which for us was of largest import. 

Of course, if sun and planets are swung free in space, an 
apparent motion of the stars may be illusory ; it might be due 
to our own motion instead. It might be the case of the Hippar- 
chan-Ptolemaic and the Aristarchan-Coppernican conceptions 
over again. Just as our earth turns about the sun, so our sun 
may be circling some central luminary lost for us in the depths 
of space, compared with which our sun may be but a minor 



HELTER-SKELTER FLIGHT OF THE STARS 321 

satellite, as our earth is a minor satellite to the sun. Our little 
system, this microcosm, may be the type, the image of the 
macrocosm ; or, more simply, we may quite leave on one side 
any question of system or solar orbits. If we conceive the 
stars, these other suns, in motion, why regard our own as fixed ? 
It may be moving too — not perhaps in an orbit, but yet some 
whither. 

It is hard most times to track out the history of an idea ; 
that of a translatory motion of our system in space can hardly 
have been very remote, at least as a scientific inference. Exist 
it might in the teeming imaginations of Bruno or Democritus ; 
it could be but a guess. It might readily have reached its first 
distinct presentation in the mind of the man who had discovered 
the periodical aberration of the stars, and therewith made clear 
the almost fathomless distances at which they must lie. It 
is to Bradley, in fact, that Humboldt accredits it. In the work 
in which Bradley announced his second discovery, that on 
nutation (1748), there is a remarkable passage : — 

" For if our own solar system be conceived to change its 
place with respect to absolute space, this might, in process of 
time, occasion an apparent change in the angular distances 
of the fixed stars ; and in such a case, the places of the nearest 
stars being more affected than of those that are very remote, 
their relative positions might seem to alter, though the stars 
themselves were really immovable. And on the other hand, 
if our own system be at rest, and any of the stars reaUy in motion, 
this might likewise vary their apparent positions, and the more 
so the nearer they are to us, or the swifter their motions are, 
or the more proper the direction of the motion is, to be rendered 
perceptible by us. Since, then, the relative places of the stars 
may be changed from such a variety of causes, considering the 
amazing distance at which it is certain some of them are placed, 
it may require the observations of many ages to determine 
the laws of the apparent changes even of a single star ; much 
more difficult, therefore, it must be to settle the laws relating 
to aU the most remarkable stars." 

But " the many ages " of observation were not needed. 
Time was going more swiftly now. It was scarce forty years, 
and not long after Bradley's death, before his ideas were put 



322 THE WORLD MACHINE 

to the solid test. Mapping, plotting, comparing the bizarre 
and bewildering movements of translation, which with his great 
reflector he can demonstrate to exist, Herschel comes at last 
to perceive or imagine that in one direction of the heavens the 
stars are slowly separating, while in the opposite direction they 
are surely coming together. You watch a herd of sheep upon 
a hillside, or a multitude of men at a distance ; they form a 
kind of blot or blur. A little nearer you begin to distinguish 
their heads ; finally you perceive that they may be all standing 
or moving about at some distance apart. As you draw away, 
the process of separation is reversed — the single units again 
become a blur. There was hardly any mistaking the meaning 
of Herschel's observation. It was that we are drawing nearer 
to the stars in one direction, flying farther and farther from 
them in another. The differences were almost inscrutably 
minute ; the detection of each single motion had been in itself 
a long and painful task. 

Moreover, the number of firmly established proper motions 
which he had to go on was very small. In his first paper on 
the subject he can use only fourteen. He did not reach his 
conclusion from the mere weight of his evidence ; the evidence 
was slight. You review the prodigious industry of Herschel, 
and you gain the impression that he may have been one of 
those tireless and unflagging investigators who lay bare the 
truth simply by grubbing. Before his journals were published 
a great many people thought this of Darwin. We forget that 
the number of grubbers is not small. That Herschel' s deter- 
mination of the direction of solar motion was something more 
is evident from the fact that it was entirely distrusted by almost 
all the astronomers of his generation. 

Curiously enough, only a few months after his results were 
published, a French observer, Prevost, reached a similar de- 
duction from another series of observations than those which 
Herschel had employed. Their results were in quite striking 
agreement ; they pointed to the idea that our system is moving, 
rather slowly as cosmic motions go, towards the constellation 
of Hercules. This point may readily be fixed by extending a 
line drawn through the three stars in the handle of the Dipper 
which lie in a straight line, to a distance about twice the extreme 
length of the Dipper itself, that is to say, to a point about equally 
distant from the Pole-star and from Arcturus. 



HELTER-SKELTER FLIGHT OF THE STARS 323 

Twenty years later Herschel made another attempt, with 
seemingly more reliable data. It is evidence of the somewhat 
speculative character of his ideas, that in his second trial he 
seems to have gone wider than in the first. The exact point 
can hardly be said to have been established even yet. We 
have now clearly determined proper motions of hundreds of 
stars, where Herschel had less than a score. A century or more 
of observation, comparing, trying out, has served only to 
confirm, broadly, Herschel's earlier results. It may be that 
the stellar apex, as he called it, towards which we are moving, 
lies in the adjacent constellation of the Lyre rather than in the 
outstretched arm of the Greek god. It is a question of but a 
few degrees ; either way the vital fact is that our solar system 
does move. The proof of this was Herschel's work. 

The direction of this translatory motion appears to be at an 
angle of about sixty degrees to the plane of the ecliptic, in which 
we move about the sun. The result of this is to cause the earth 
to describe in the heavens, a spiral path. It might crudely be 
illustrated by a bed-spring leaning over to one side. It is 
perhaps worth noting that this corkscrew flight of the earth 
does not produce a motion tending progressively to turn the 
heavens upside down as some muddled minds have conceived. 

Herschel made more than one attempt to determine the 
velocity of solar motion ; obviously the available data were 
scant. It is of some interest that his conclusion was that ** we 
may in a general way estimate that the solar motion can certainly 
not be less than that which the earth has in her annual orbit." 
This is nineteen miles a second. The latest calculations do not 
vary greatly from this figure. For a time it was supposed that 
the sun was careening through space with a rush ; some estimates 
put it as high as a hundred and fifty miles per second. It now 
seems likely that it is not much more than ten or fifteen miles, 
somewhere probably between these two. In this view the 
annual displacement of the solar system is a little more than 
double the diameter of the earth's orbit, or only about a tenth 
or fifteenth part of the diameter of the system itself. 

Obviously if the stars were " fixed " it would require an enor- 
mous range of time before this displacement would be sufficient to 
cause any appreciable difference in the appearance of the firma- 
ment. So, too, it will be a long time before we shall be able to 
determine the larger question as to whether the motion of the 



324 THE WORLD MACHINE 

sun is a mere aimless flight, no whither and no whence, or 
whether it be describing a curve about some central point. 

The surmise of a circular motion was natural. The revolu- 
tion of the planets, the quantity of satellites which in turn 
revolve about them — possibly, for aught we know, the satellites 
themselves may have their little moons — obviously suggested 
that this wheel-within-a-wheel arrangement is characteristic of 
the whole cosmic order. As yet there is no evidence pointing 
towards a central sun, but the idea that such a sun exists was 
considerably strengthened by another of the long list of dis- 
coveries made by this same wonderful man. 

As Bradley's hunt for minute movements of parallax had 
led him to the discovery of aberration, so Herschel's researches 
in the same field led him to the discovery of the double stars. 

Galileo had long before pointed out that the stars most 
advantageous for the discovery of a possible parallactic shift 
are those which lie in almost identically the same line of sight. 
The swing of the earth in its orbit would certainly produce a 
larger and more easily detected change of position in such a 
pair of stars than those more widely separated. Following this 
hint, Herschel set about making a catalogue of such doublets. 
One day the idea came that this closeness of position was not 
a mere accident resulting from the especial angle under which 
we see them, not a mere coincidence, as, for example, when a 
pair of mountain peaks happen to lie in the same line of view 
from where we are standing. The number of these coincidences 
was far too great. Laplace and others were then engaged in 
making the calculus of probabilities a fashionable study. The 
simplest computation from the laws of chance sufficed to show 
that alike the nearness and frequence of these pairs of stars 
was far greater than would occur from any random distribution. 

So absorbing was their study that, as the difiiculties of 
establishing any angle of parallax became more and more clear, 
Herschel gave over his attention to these perplexing appear- 
ances. Finally his reward came. It had been for some time 
known that the bright star which we call Castor, of the constel- 
lation of the Twins, is in point of fact two stars, so nearly in the 
line of sight that they appear to the eye single. From a long 
series of observations, supplemented by another by Bradley 
of many years before, Herschel was able to perceive a minute 
change in the position of the two stars, such as to leave little 



HELTER-SKELTER FLIGHT OF THE STARS 325 

doubt that they were in reahty revolving, one around the other. 
With this clue he set about searching for others : he found 
half-a-dozen. His observations enabled him to attempt a 
rough guess at the periods of their revolution ; that of Castor 
and its twin he put at three hundred years. It has slowed down 
since ; the present estimate is about a thousand years. 

From this small beginning the number of double stars, or 
Binary Systems, as they have come to be called, has grown 
until they are now numbered by the hundreds. Their discovery 
naturally led to a search for triple and multiple systems. The 
probable existence of such multiples is no longer a matter of 
much question. So it was that Herschel's studies opened the 
way for some insight as to the structure of the universe. It 
was this latter which eventually became the especial predi- 
lection of his Hfe. 

But the heavens show something more than stars. Just as 
here and there appear little clumps and clusters, so even to 
the unaided eye there are here and there faint blurs which do 
not seem to be made up of distinct stars. The old-time observers 
had given to these the name of nebulae or clouds. The first 
effect of the introduction of the telescope was to resolve these 
star clouds in part into star clusters ; naturally it was supposed 
that telescopes of higher power would resolve them aU. Even 
before Herschel's time, such a view was found to be erroneous. 
Several astronomers just preceding him had begun to catalogue 
the nebulae, with the idea of eventually determining their density 
and the changes that might take place in them. One of these 
observers was Messier, whose specialty was hunting comets. 
It was often very difficult to distinguish a comet from a nebula, 
so he made a record of over a hundred of these puzzling appari- 
tions. This was where the matter stood when Herschel took 
it up. 

Before he had done he had catalogued twenty-five hundred 
— disclosed, as well, their extraordinary variety. What was 
still more of interest was that he came to conceive them as the 
stuff from which suns and stars are made. He found them of 
aU shapes and sizes, some bright and some dull, some with a 
seeming nucleus in the centre, some like cloudy stars surrounded 
by a nebulous atmosphere. As he phrased it, he found that 
they could be selected " so that an insensible gradation shall 



326 THE WORLD MACHINE 

take place from a coarse cluster like the Pleiades down to a 
milky nebulosity like that of Orion, every intermediate step 
being represented." At first this led him to the idea that 
eventually they might all be dissolved into stars. Later on, 
as we shall find, he put aside this view, to regard them as floating 
islands of starry mist. 

Herschel did not exhaust the possibiHties of stellar research, 
though so it must have seemed when he died. He Uved to a 
splendid age ; he left a son nobly to carry on his work. The 
life with which his own may best be likened is Galileo's. He 
did for the larger universe of the stars what the Tuscan had 
done for the immediate portion in which we dwell. Theirs 
undoubtedly was a wonderful opportunity. But it was open 
to others. That is why in the records of this world the account 
of genius — the departure from the normal, essentially imitating, 
uninnovating mind — must always be large. 

Our debt to them is great. Consider how vast a revolution 
had been wrought in the thoughts of mankind within the brief 
span of the life and death of these two men and we shall hardly 
begrudge their fame. It was a period of but little more than 
two centuries. Within these two centuries the race had gained 
a larger, more precise, more vivid idea of the realities of creation 
than, let us say, in the two hundred centuries or more that 
we may consider civilisation — a relatively high civilisation, in 
point of speech and manners and the conveniences and trappings 
of life — to have endured. 

Yet in a larger sense it was not their work. It was the 
work of an instrument — in rounder phrase, of a machine. With- 
out the telescope, Galileo and Herschel — yes, and Newton and 
Laplace and all their kind — were as babes on a deserted barque 
drifting the ways of the sea. Think of what were our ideas 
without it ; consider what an utter havoc it wrought in all 
man's primitive impressions and ideas. When Galileo lifted 
his first telescope to the sky, there was naught save the geo- 
metrical constructions of a priest to disturb the repose of the 
earth. Men trod upon a globe solid and unmoving, and beneath the 
unhasting heavens. " Unchanging as the stars " was a synon3nii 
of the time. When Herschel died, men lived upon a whirhng 
earth, shooting incredibly through space ; this earth but a 
point turning round about one of fifty million suns. The optic 
tube had confirmed wild conjecture, had reached far beyond 



HELTER-SKELTER FLIGHT OF THE STARS 327 

conjecture into the realms of dream. Neither earth nor sky 
nor suns stand still. There is nothing fixed, nothing at rest. 
The suns are tumbling headlong, shooting each whither, upwards, 
downwards, in every direction, dragging with them their progeny 
of helpless satellites. 

Could Lucretius return, could his intellectual godfather, 
Democritus, come again among men, how marvellously they 
would find their previsions fulfilled ; for, seen through the eye 
of the telescope, is it not, as their vast imaginations conceived, 
less a cosmos than a chaos into which we are born, wherein 
there seems nothing but blind confusion, a hopeless disorder, 
a wildly scattered rout, a drunken revelry of dancing suns ? 



CHAPTER XXVI 

THE MEASURE OF STELLAR SPACES 



Praeterea, si jam finitum constituatur 
Omne quod est spatium, si quis procurrat ad oras 

Ultimus extremas, jaciatque volatile telum, 
Id validis utrum contortum viribus ire, 

Quo fuerit missum, mavis, longeque volare, 
An prohibere aliquid censes obstareque posse ? 

Alterutrum fatearis enim sumasque necesse est ; 
Quorum utrumque tibi effugium praecludit, et omne 

Cogit ut exempta concedas fine patere. 
Nam sive est aliquid, quod probeat ef&ciatque 

Quo minu' quo missum est veniat, finique locet se, 
Sive foras fertur, non est a fine profectum. 

Hoc pacto sequar atque, oras ubicumque locaris 
Extremas, quaeram, quid telo denique fiat. 

Fiet uti nusquam possit consistere finis, 
Effugiumque fugae prolatet copia semper. . . . 

Lucretius, De Rerum Naturd, I. 967. 



S'il est une limite a cette immensite. 
Imagine un archer, qui de I'extremite 

Decroche avec vigueur une fleche rapide ; 
Admets-tu que le trait parte en I'espace vide. 

Qu'il vole sans que rien soit la pour I'arreter, 
Ou bien a quelque obstacle ira-t-il se heurter ? 

II faut faire ton cboix, et ta raison captive 
Ne pouvant s'echapper de cette alternative 

Sera, tu vas le voir, contrainte d'effacer 
La borne qu'a I'espace elle pretend fixer 

Car soit que quelque chose intercepte a distance 
Le fleche, soit que libre au loin elle s'elance, 

Tu vois bien, en prenant I'un ou 1' autre parti, 
Que le bord n'etait pas d'ou le trait est parti. 

Avance, si tu veux, avance ta limite, 
Tu ne peux m'eluder ; de poursuite en poursuite 

Je t'arrete et je dis : que devient notre trait ? 
Ainsi tou jours, tou jours ta borne avancerait, 

Et partout a 1' archer, n'importe ou tu le places, 
L'immensite sans fin ouvre d'autres espaces. 

Traduction de M. Martha. 



CHAPTER XXVI 

THE MEASURE OF STELLAR SPACES 

If the truth be the highest thing for which man may strive, 
it surely seems to follow that we should award to seekers for 
the truth a special place. So, in a way, mankind has always 
done, first among savage tribes, to the medicine man ; in later 
days, when his view widened to the inclusion of moral problems, 
to the priest ; later still, when he had begun to reflect upon the 
larger enigmas of existence, to the philosopher ; in our own 
day, when the thing of utmost worth seems the reality, to the 
magi of science. But if the things revealed by these later-day 
workers of magic be worth while, if humanity has been broadened, 
its aims exalted, if its primitive savage instincts to hurt and to 
kiU, to maim and destroy, have been repressed or diverted, 
then surely we owe a debt to those who have supplied the means 
by which the miracle has been wrought. 

It is a commonplace that all our knowledge of the world 
in which we live, its surroundings, its nature, its extent, has 
been derived from mechanical appliances. Then it is not to 
Galileo, the user of the telescope, but to Galileo the deviser, 
and to his obscure forerunners in Holland, that the greater 
debt is due. Insufficiently do we do honour unto him who con- 
trives, who constructs, who invents, who improves. In the 
instance immediately at hand it was the instrument- maker 
who made it possible to work out the ranges of the stars. Scores 
and even hundreds of assiduous astronomers had tried it, but 
to no end. They had conceived many ingenious and round- 
about ways ; perhaps two of these are worthy of record. 

The new star that roused Galileo to his first great battle 
for the Coppernican system — the new star of 1604 — had like- 
wise deeply engaged the attention of Kepler. He saw it first 
in October. By January it had begun to wane. When October 
came again it had disappeared from view. It was certainly 

a star. This Kepler could be sure of, because within this year 

331 



332 THE WORLD MACHINE 

his point of view had been shifted from one side of the earth's 
orbit to the other and back again, and still he could observe 
no change of position in the star, relative to its neighbours. 

If yet unable to fix its distance, Kepler bethought himself 
of a method that might at least determine the lower limit. 
His idea was simply this : The outermost of the planets then 
known completes its orbit in a little less than thirty years. 
In a year, then, Saturn passes through an arc of about twelve 
degrees of its circle ; in six months, half this. The position 
which it should occupy against the bank of stars may then be 
determined accurately for any desired moment. But if Saturn 
be observed from the earth at intervals of six months — that is 
to say, from one side of the sun to the other — its apparent 
shift of position averages about six degrees. And its distance 
from the earth is known. 

Kepler estimated that the limits of error in observation 
attained in his time certainly did not surpass two minutes of 
arc. If, therefore, no shift like that of Saturn could be dis- 
covered for the new star, it follows that it must be as much 
more distant as six degrees are greater than two minutes. This 
was i8o times. Saturn being ten times the distance of the 
earth to the sun, it was clear that the new star was at least 1800 
times this distance. The same method was, of course, applicable 
to any star, and as the limits of possible error were steadily 
reduced, this lower limit of distance was steadily raised. 

It had reached at least ten times 1800 earth- distances when, 
fifty or sixty years later, the fertile mind of Huyghens caught 
up the problem from quite another point of view. By that time 
the ancient plan of classifying the stars according to their relative 
brightness had been taken up anew. Through the aid of the 
telescope they were able to fix this relationship with a far greater 
accuracy than anything hitherto known. Accustomed to such 
minuteness of observation, Huyghens conceived the idea of 
comparing the brightest of the stars with the sun. To effect this 
comparison he placed across the end of his telescope an opaque 
disk, which he pierced with a pin-point. Turning his tube now 
towards the sun, he found that its brightness, shining even 
through this minute aperture, vastly exceeded that of Sirius. 
Decreasing the aperture yet further by means of a small objective, 
Huyghens calculated that he must reduce the diameter of the 
sun 27,000 times in order to bring it down to the brightness 



THE MEASURE OF STELLAR SPACES 333 

of Sirius. It followed from this that if they are the same in 
size or light-giving power, Sirius is at least 27,000 times the 
distance of the sun. 

The computation was vague ; it was, after all, an estimate 
and not an exact measure, and it was an exact measure which, 
with the splendid advance of the science in other fields, now 
became the goal of stellar observers. 

About the time that Bradley, despairing of any direct de- 
termination, had turned his attention from questions of parallax 
to that of the proper motion of the stars, an idea occurred ap- 
parently to several minds which was to bring the solution of 
the problem. One of these was a young Englishman named 
Savery, fated, like Gascoigne, his predecessor in this immediate 
work, like Fraunhofer, who was to follow him, to show a brilliant 
promise, to do a brilliant work, then to be cut off before he could 
enjoy its fruits. He had suggested a recondite method of working 
out stellar parallax from observations of the aberration and 
velocity of light ; in practice it failed, from the extreme com- 
plexity of the problem. 

He turned from methods to instruments ; the device he 
imagined — it seems independently to have occurred to a French 
contemporary, Bouguer — was not less ingenious and of far 
greater value. It was simply the notion of having a sort of 
binocular telescope with a single tube, showing two distinct 
images ; it was so constructed that the images could be sepa- 
rated or superimposed at the will of the observer. From this 
it was possible to measure exceedingly minute angles. Perfected 
in the hands of the famous instrument-maker Dollond, the 
object-glass was simply cut in twain and mounted so that one 
half might be made to slide past the other. As imagined by 
Bouguer, the device was intended for the measure of the hori- 
zontal diameter of the sun ; it thence derived its name of the 
heliometer, or sun-measurer. 

So it remained, with but little wider application, until it 
was taken up by a young German optician, Fraunhofer. He 
had started out as an apprentice for a looking-glass maker, 
deadly poor, with no parents and no one to help. He revealed 
a genius for grinding and polishing mirrors and glasses ; eventu- 
ally he rose to be the head of the optical department of a great 
Munich firm. His name is more familiar as it is attached to 



334 THE WORLD MACHINE 

the well-known Fraunhofer lines in the spectral image ; it was 
his careful maps which first gave them prominence. But his 
greatest deeds were his instruments. Two of his most beautiful 
constructions were the famous Dorpat refractor and the Konigs- 
berg heliometer, set up in 1829. The latter was essentially 
an equatorial telescope, designed on the Dollond plan of a 
divided object-glass, and provided with micrometer screws, 
permitting of angular measurements of an unheard-of accuracy. 

At this time the head of the Konigsberg Observatory was 
the celebrated Bessel, with a brilliant record as an observing 
astronomer, author of a vast work of tabulation, the Fundamenta 
AstronomicB, and keen to prove the powers of his new instrument. 
As far back as 18 12 he had made an especial study of a double 
star in the constellation of the Swan, known in the catalogues 
as 61 Cygni. It was not a brilliant star — it is invisible to the 
human eye^but it had been found to have a relatively rapid 
motion across the line of sight. It had been studied by other 
astronomers after Bessel. Arago had spent a great deal of time 
upon it, with the merely negative result of determining that 
its parallax must be less than half a second. This meant that 
it must be more than four hundred thousand times the distance 
of the sun ; how much farther no one could say. At the Cape 
of Good Hope, Henderson, with a fine instrument, was taking 
observations upon a great double star of the southern hemi- 
sphere, the alpha star of the Centaur ; Struve was busy at 
Dorpat. It seemed certain that some sort of a result would 
be reached soon ; as yet they were little further advanced 
than Hooke in the seventeenth century or Herschel or Bradley 
in the eighteenth. 

When Bessel turned his great new heliometer on the swift- 
flying star of the Swan again, he must have felt that the goal 
was very near. He says himself that he did not know whether 
the measurements of its angle would turn out to be tenths 
or thousandths of a second of arc ! Consider for a moment 
what this means. The dial of your watch is divided into sixty 
spaces, each representing a minute. Cut each of these into 
six and you have the three hundred and sixty degrees which 
make up the astronomical circle. Division of each degree by 
sixty gives astronomical minutes ; by a sixty again gives astro- 
nomical seconds. A tenth of such a " second," then, is not a two- 
hundred-thousandth part of the space crossed by the watch 



THE MEASURE OF STELLAR SPACES 335 

hands each minute of time ; a thousandth of a " second " is less 
than a twenty-milhonth part. 

One has perhaps a httle better idea of the accuracy attained 
when he thinks of looking through a slit at the far end of a tube, 
the slit the breadth of a thin knife-blade — say, the hundredth 
of an inch — the tube more than half a mile long. The sht would 
represent a tenth of a second of arc, of which one degree would 
cover thirty feet. These are the units, the subdivisions of the 
gauge, with which Bessel and his successors worked. 

Observations taken from August 1837 to October 1838 led 
him to a parallax for 61 Cygni of ^^ of a second. This meant 
nearly six hundred thousand mean distances of earth to sun. 
It meant that light, travelling six hundred and sixty million 
miles per hour, would require nine and a half years to cover the 
intervening space. The distance has since been slightly re- 
duced. But nearly seventy years of minute observation, by 
many different astronomers in different parts of the earth, 
have changed Bessel' s result but little. He had at least reached 
a figure which could stand. The long puzzle was at an end. 
Here at last was a star whose distance was known. 

Curiously enough, as so often happens, the solution would 
have come from other hands within not more than a year. Com- 
bining the observations of Henderson in 1832 with others made 
in 1839, it ^^^ found that there was a star much nearer than this 
No. 61 of the Swan. This was the now familiar alpha Centauri, 
the third brightest star in the heavens, but unseen by our 
northern eyes. Its parallax was originally calculated at o''.9i, 
or nearly a second. Subsequent reckonings have reduced this 
somewhat ; it is now set down at 0^^.75. This indicates a dis- 
tance of 4.4 light-years. Seventy years of observation, again, 
have failed to disclose any more proximate sun. 

About at the same time, Struve at Dorpat announced a 
paraUax of a quarter of a second for Vega. Somewhat earlier 
he had estimated that of the alpha star in the Lyre at between 
o'^.i and o''.2 of a second. After two years of observation, 
Peters, at Pulkowa, gave o''.i as the paraUax of Polaris. This 
figure is slightly too great ; it is probably not more than o'^oG, 
answering to a distance of forty-four light-years. This is still 
about at the limit of certain parallactic measure. It is pain- 
ful work ; less than a hundred are yet known with sufficient 
precision to permit of any confidence in the results. This is 



336 THE WORLD MACHINE 

hardly more than an average of one a year since Bessel's 
day. 

Still, it is a beginning — enough to make certain that a true 
parallactic shift of the stars may be found, has been found. 
What Aristarchus, what Tycho, what Galileo, what Hooke, 
Halley, Bradley, Herschel, and a long line of investigators could 
not discover, Struve, Bessel, and Henderson had attained. 
They swept away the last objection that might lie against the 
Aristarchan-Coppernican scheme. For all thinking minds Brad- 
ley's discovery of aberration, the queer little annual shift of the 
stars in their places, had been definite proof. In no other way 
than by supposing the annual motion of the earth could this 
indubitable shift be explained. There could, indeed, be little 
doubt in an intelligent mind after Cassini's demonstration of the 
true distance and grandeur of the sun. It was whoUy incon- 
ceivable that a body a million times the bulk of the earth should 
revolve about our midget planet. 

After 1840 or 1850, when the results of Bessel and the others 
had been fully confirmed, doubt became mere obtusity. Human 
certitude can never be absolute ; it can only approach infinite 
probability. It is practically infinite probability that the truth 
of the Coppernican theory will never be seriously questioned 
again so long as the world shall last. 

The discovery of steUar paraUax brought more than simple 
proof of theory ; it gave us our first insight into the true grandeur 
of the stars. 

So long as man had no means of knowing their distance, 
it was open to suppose that the brighter stars are the nearer 
stars, that they are all more or less of a size. It was equally 
open to suppose that they were all at the same distance — a 
very great distance, no doubt — and that they vary in size as 
they vary in brightness to our eyes. Neither supposition in 
any wise represented the fact. 

The nearest star, alpha Centauri, as convergent lines of study 
make clear, is something very close to a duplicate of our own 
sun. It is about the same in size, temperature, and brightness. 
We may therefore suppose that its evolution has been very 
nearly parallel to our own. It is not very fanciful to think 
that the discovery of the nearness of our sun was made upon 
one of the planets of alpha Centauri at about the same period 



1 



THE MEASURE OF STELLAR SPACES 337 

as the determinations of Henderson and Bessel. We should 
allow always for a possible error of a few million years. Our 
sun would appear a star of the first magnitude to them, as does 
alpha Centauri to us. 

At about twice the distance of alpha Centauri is No. 61 
Cygni. It is of the fifth magnitude. Clearly, then, unless it 
be of an utterly different constitution, it is very much smaller 
than alpha Centauri or our sun. Its actual brilliancy appears 
to be not more than one-tenth that of the sun ; it may not be 
one-third the latter's diameter. 

At about the same distance, between eight and nine light- 
years, is the great Dog-star. Sirius is nearly three times as 
bright as alpha Centauri, ten times as bright as 61 Cygni. The 
light it gives is perhaps thirty times that of our sun. Its bulk, 
if its temperature were the same, would therefore be more than 
a hundred times the bulk of our sun or of our nearest neighbour 
star. 

Again, outshining any other star in the northern heavens, is 
huge Arcturus. It is fifteen or twenty times more distant than 
the Dog-star, and still more vast. The light it sheds would be 
equal to that of perhaps one thousand three hundred of our 
suns. It is apparently a solar type of star ; its bulk, therefore, 
must be three or four thousand times the volume of Sirius, perhaps 
forty or fifty thousand times the volume of our luminary. 

Apparent magnitude is therefore but little index of the reality. 
This conclusion is still further borne out by the amazing example 
of Canopus, the great star of prehistoric Egypt. It is the 
brightest of the southern heavens, second only to Sirius. Recent 
careful determination reveals the fact that it has no appreciable 
parallax, as it has no appreciable proper motion. The present 
limits of error are in the neighbourhood of a few hundredths 
of a second. Sir David Gill sets the distance of Canopus at a 
minimum of two hundred and ninety-six light-years. It is 
apparently situated among stars of the eighth magnitude, if 
not farther. In order to shine at its present brilliancy from 
this distance, it must have ten or fifteen thousand times the 
luminosity of our sun. At this distance our sun would long 
have ceased to be visible to the naked eye. 

Canopus is, again, a solar type of star ; its density and 
temperature is, then, somewhere near the sun's. Consider the 
inference. At the same temperature the amount of light shed 

Y 



338 THE WORLD MACHINE 

by a star is dependent simply upon its surface. Surfaces are 
in turn proportionate to the square of the diameter, volumes 
to the cube. If Canopus gives out more than ten thousand 
times the light of our sun, it follows that its diameter is more 
than a hundred times that of our sun ; that is, perhaps more 
than a hundred million miles in diameter. This would mean 
a sun, a body, the distance from whose centre to circumference 
would be four hundred times the distance from the earth to the 
moon ; it would be greater than the distance from the earth 
to the sun. It would be so vast that within its almost un- 
imaginable shell the earth and all the inferior planets might, 
in the absence of a deterrent medium, pursue their orbital ways. 
On present reckonings, its volume is perhaps a million and a half 
times that of our central orb. 

Reflect that the sphere of the sun would contain a million 
of our little earths ; then that, on the estimates given, the 
sphere of Canopus would hold more than a million suns, more 
than a million million earths. 

All this, it is to be remembered, is simply the apparent 
lower limit. How much more vast it may be we have no means 
of knowing. Already the mind reels in its endeavour to com- 
prehend a body, a single mass, of such stupendous dimensions. 
Even the greatest of the telescopes probably do not reveal more 
than a hundred million stars. If we were to suppose that they 
were of something the average size of our sun, then Canopus 
would swallow a million of them. And, for aught we now 
know, Canopus may be a hundred, a thousand, a million times 
vaster still. It seems probable that some of the stars are 
distant more than thirty thousand light-years. If the great 
sun of Argo be as far away, its bulk would necessarily be that 
of a million million suns to give us the light it does. 

Nor have we any reason to suppose that this colossus is 
the greatest object in the universe. There are at least two 
other stars known, which may be as large, or larger, than 
Canopus. One of these is Rigel, the second brightest star in 
the constellation of Orion ; the other Deneb, the brightest star 
of the constellation of the Swan. Like Canopus they yield 
no appreciable parallax, yet their luminosity is so great that it 
must be thousands of times that of the sun. 

Consider now that these estimates of actual brilliancy, that 
is to say, of the true grandeur of the stars, is dependent upon 



THE MEASURE OF STELLAR SPACES 339 

their supposed distance. Consider that the parallax is known 
of sixty stars out of perhaps a hundred million revealed by the 
photographic plates. Consider that merely a beginning has 
been made, and it is easy to see that any endeavour to fix an 
upper limit is simply absurd. It is conceivable that gigantic 
suns may exist, compared with which even huge Canopus would 
seem a pigmy, and compared with which our solar deity would 
be as insignificant as one of the five hundred asteroids which 
circle out beyond the path of Mars, to us. There may be not 
merely one, there may be many. 

We have no distinction as to vastness, we have none of little- 
ness, even. Just as it is clear that there are suns hundreds, 
perhaps millions of times the bulk of our sun, so it appears 
that there are others, probably, beside which we might seem 
very huge and very important. The universe, then, is not made 
up of units of a regular pattern, of much the same grandeur ; 
there is no evidence of set design, no evidence of the existence 
of a mould for suns and worlds. The stars differ among them- 
selves in size as much, perhaps, as the components of our solar 
system, the individual planets and their satellites, even, differ 
among themselves. 

The moral is not distant ; it is not flattering. What is 
demonstrated beyond a doubt is that in the firmament of stars 
our solar system is of no especial consequence. It is not unique, 
it is one of hundreds of millions. It is not enormously vast ; 
it is merely mediocre. It seems to have absolutely nothing 
about it that is distinctive. It is one of a crowd, a mob, a 
multitude, an infinite swarm. This is the social, the moral, the 
anthropological lesson of the measures of stellar distance. 

If you wish to picture it, you may conceive it in the simile 
already adduced, that of one of a cloud of dancing fire-flies — 
a cloud hundreds of miles in extent. If it will be a better help 
to the mind, we may think of a huge mountain, streaming with 
millions and billions of ants. One of these ants, one of these 
fire-flies, would be our sun. It is in some such way, perhaps, 
that we may estimate the importance, not of the little life of 
man, not of the minor planet that we call the earth ; but of 
the whole solar system and all that it contains. 

The stars move ; that Herschel had made clear. Like the 



340 THE WORLD MACHINE 

earth, like the sun, they are flying, flying, flying. Is there any 
way that we can compute their speeds ? 

In front of the window near where I write, Ues the Golden 
Gate of the Pacific, famed in the legends of the newer Argonauts. 
Across it, as I write, a ship sails slowly. Its distance, the width 
of the Gate, are known. It is needful only to time its passage 
to know how fast the ship is sailing. It is the same with the 
stars whose distance we know. 

Bessel had chosen the star numbered 6i Cygni, for measure 
of its parallax, because of its relative rapid motion across the 
line of sight. When he had computed its distance it was not 
diflicult to reckon its speed. It came out at nearly forty miles 
per second. As cosmic motions go, it was not great. Some of 
the planets, some of the comets, move as swiftly. But consider 
that this star is not a planet, not a tenuous comet. It is a sun ; 
it is doubtless carrying in its train a company of satellites like 
unto our own system. 

It taxes the imagination to conceive even the rate of motion 
of our own earth. One can count five, at the utmost ten in 
a second. In each of these counts our earth has flashed on 
several miles along its pathway around the sun. The star in 
the Swan that we number 6i is moving twice as fast. You may 
multiply the speed of the earth by ten ; and there are stars 
moving more swiftly still, one of them the greatest star of the 
northern firmament. 

The first of these terrific speeds to be discovered was the 
celebrated " run-away " star known as 1830 Groombridge — that 
is, a star otherwise so insignificant that it has merely a number 
in the Groombridge catalogue. It is apparently moving at 
somewhere near two hundred miles per second, perhaps more. 
The vast sun of Arcturus is moving more swiftly still. Some 
recent estimates set its speed at between four and five hundred 
kilometres, possibly three hundred miles or more per second. 
So far as we know, there is nothing like it in the universe. Of 
the stars whose speeds may be reckoned there is nothing ap- 
proaching it save in the instance named. Most of those that 
are known move at comparatively moderate speeds like our own 
sun. But our knowledge of the steUar universe as yet is slight. 
For aught we know, there may be others whose rate of trans- 
lation is vastly beyond that of Arcturus itself. 

Three hundred miles per second ! Let us try a minute to 



THE MEASURE OF STELLAR SPACES 341 

conceive it. Here is a body, possibly three or four thousand 
times the diameter of the earth. If its density be somewhat 
similar to that of our sun, its mass then is perhaps a hundred 
or two hundred million times that of the earth. The energy 
of a moving body is proportionate to its mass first, and secondly, 
to the square of its speed. A rifle-bullet moving at less than 
half a mile per second, and striking a steel target, becomes 
very hot. At a dozen times this speed it would develop enough 
heat to melt itself. 

Arcturus is moving six hundred times as fast. Were it to 
collide with a stationary object, it would develop then thirty- 
six thousand times as much heat per unit of mass as the rifle- 
bullet. We have then an idea of what stellar collisions may 
mean. Arcturus has, let us say, forty to fifty thousand times 
the attractive force of our sun. It would draw another sun 
or planet towards it with proportional speed. 

There is some evidence that such collisions take place. It 
is doubtful if the nearness of our nearest star is exceptional. 
Were Arcturus at the distance of alpha Centauri, and coming 
towards us, it would need but two or three thousand years to 
cross the intervening space — a fraction of a second in the life- 
history of the stars. Assuming that the average spacing of the 
suns is not much greater — it may be much less — it is evident, 
with many hundreds of millions of them flying each whither 
at tremendous speeds, such collisions might be frequent. As 
we shall see upon a later page, it is probable that they are. 

Estimates of such unthinkable motions of colossal masses 
might well raise a doubt as to their reality. At three hundred 
miles per second, a body several miles in diameter flashing 
across the line of sight a few feet before our eyes, would move 
so swiftly that it would not be perceived. In our endeavour 
to obtain a mental presentation of the motion of such a mass 
as Arcturus, we might well believe that the observations were 
an error, or the whole idea an illusion. Happily there came 
a discovery which was not only to confirm the fact of stellar 
motion ; but to disclose that motion, when it lay directly in 
and not across the line of sight. It was to do much besides. 
It came within a few years of the disclosures of Bessel and 
Struve, though it was not put into effect for many years there- 
after. It was from such a strange quarter of the sky that men 
could scarcely then believe, and the wonder has not yet ceased. 



CHAPTER XXVII 

THE SPECTROSCOPE AND THE STUFF OF 
COSMOS 



Was hier im Raume spukt ! 

Erman. 



CHAPTER XXVII 

THE SPECTROSCOPE AND THE STUFF OF COSMOS 

If we look back upon the gradual advance of human know- 
ledge, we might almost be led to conceive physical investiga- 
tion as a kind of game of Hare and Hounds. The hand of 
nature, as it were, scatters the bits of paper which have en- 
abled her followers to pursue her track. But sometimes the 
scent has been so thinly sown, the gaps so far between, 
that baffled man might have felt as though nature had not very 
fairly played the game. Perhaps it has added a certain zest ; 
it has certainly demanded a sharpness of observation, a patience, 
and a genius of intuition, compared with which the interesting 
problems of Mr. Sherlock Holmes seem elementary. 

Certainly no puzzle was ever set the mind of man to solve 
seemingly more elusive than the lines which cross the coloured 
band formed when a thin beam of sunlight is turned through 
a prism. As the band is spread wider and wider, the number 
of these dark lines runs up into thousands ; they seem dis- 
tributed in no regular order, they appear and disappear under 
different physical conditions, in seeming hopeless confusion. 

Surely no phenomenon was ever better named than when 
Newton spoke of this prismatic band as a spectrum — a spectral 
apparition. Could Newton have been told that out from all 
this tangle we should one day learn the constitution of the 
sun, of the stars as well — their temperature, their motions, 
their physical states, even that dreamer of wonderful dreams 
would have sagely shaken his head. How has all this mar- 
vellous accession of knowledge come ? 

In Newton's time men had settled down to think of light 
as a substance, that it was due to the emission of infini- 
tesimal particles, which bombard the eye with incredible speed. 
Newton's contemporary, Huyghens, had a different idea, that 
light was not material at all, but, like sound, a form of wave 

345 



346 THE WORLD MACHINE 

motion. Though Newton gave his adhesion, finally, to the 
'* emission " theory, the pages of his Opticks are full of evi- 
dence to show how often he inclined to the alternative view. 

The theory held its ground, though with increasing difficulty, 
as one new observation after another was made, for a century 
or more, and until it came under the keen scrutiny of an English 
physician, Dr. Thomas Young. The latter showed that by 
pricking a pair of pin-holes, close together, in a piece of paper, 
the two little pencils of light which come through, when spread 
out upon a screen, appear coloured in the interval in which 
the rays from the two openings cross each other. Very much 
the same appearance may be noted on very thin soap-bubbles. 
Black spots appear which, from having been studied by old 
Sir Isaac, are known as Newton's rings. The fact could only 
be explained by the idea that the rays in part mutually ex- 
tinguish each other. Further experiments with very thin plates 
left no doubt as to the interpretation. 

Evidently, then, light was not a material substance ; it 
was inconceivable that one little shower of particles could abolish 
the other in this curious way. If light were immaterial it must 
be then some form of motion, since there was no other way 
by which the transmission or propagation of light could be 
explained. Huyghens, it seemed, had the right of it all along. 
It was some little time, however, before the conclusions of 
Young, independently reached a few years later by a young 
French physicist, Fresnel, could penetrate the understanding 
of the academic authorities ; it is generally so. This was in 
the first ten or fifteen years of the new century. A generation 
later, and in a new generation with fresh eyes to see, a second 
crucial test, by Foucault, brought conviction. 

Then it was that the investigators began to consider with 
a larger insight the dark lines which cross the spectral band 
of sunlight. They had been roughly mapped by Wollaston, a 
co-worker with Young ; with . more care by Fraunhofer, the 
celebrated telescope -maker of Munich. It had been noted very 
early that the spectrum of ordinary gaslight, for example, does 
not show these dark lines ; the gradations of one rainbow colour 
into another are not interrupted; the spectrum is continuous. 
Again, it was found that if some of the elementary gases, like 
those which compose water — for example, oxygen or hydrogen 
— were illuminated by an electric spark, their spectral bands 



SPECTROSCOPE AND STUFF OF COSMOS 347 

showed only a series of bright Hnes, and not the whole rain- 
bow spectrum, hke the sunlight. Moreover, these bright bands 
seem to vary with the different substances employed. Finally, 
soUd substances, rendered incandescent, gave varying dark-line 
spectrums. It seemed as if each substance produced its own 
characteristic apparition. 

Evidently here was a capital discovery. The light of the 
spectrum comes from a distance. That distance may be half 
a foot, a few feet, a few miles, it may be millions of miles. So 
long as the light passes through no absorbing medium the 
spectrum remains the same. What if this were true even of 
the light of the sun ! It was first needful, of course, to sift 
out all the disturbances due to purely earthly conditions, to 
atmospheric absorption, and the like. If this could be done, 
then it might be possible to compare the spectrum of the sun 
with the spectrum of the various elements, and so determine 
the materials which make up that glowing disk of light. 

Such a possibility floated before more than one mind, notably 
Sir John Herschel's, but the solution came from a German 
physicist, Kirchhoff, working in conjunction with the celebrated 
Bunsen. One day, passing a ray of sunlight through vaporised 
sodium, one of the constituents of common salt, he noted that 
the characteristic bright lines of the spectrum of sodium had 
disappeared. He saw in a trice that he had made an observa- 
tion of profound import. Following it up, he was able to show 
that when a gas grows cold it will absorb the same rays of light 
which it emits when it is incandescent. 

The dark lines of the solar spectrum mean, therefore, that in 
the sun are many of the earthly elements sending us their charac- 
teristic light, but sending it through an atmosphere of cooler gas, 
which absorbs these rays, and produces the dark lines we see. 

This was the essence of Kirchhoff's discovery. The broad 
facts were simple enough ; the details were infinitely puzzling. 
Of a truth, spectrum analysis, as this study has come to be 
called, has developed a wondrous and ofttimes precarious 
delicacy. Sometimes it has seemed as if the apparent contra- 
dictions, the inexplicable anomalies that have appeared as the 
study developed, were likely quite to vitiate any certainty of 
inference. Patience and persistence, however, have told, and 
the typical German textbook on the subject now comprises 
three huge volumes. It is to-day a special science. 



348 THE WORLD MACHINE 

Latterly the camera has proved a wonderful aid. Instead 
of trusting merely to the momentary impressions of the eye, 
it is possible to photograph the varying spectra with accuracy ; 
moreover, to follow the spectrum out beyond the range of the 
eye into the so-called ultra-violet portions, whose rays affect 
only photographic plates. These spectrograms make possible 
measures and comparisons which would be quite impossible to 
the unaided eye. Likewise they may be copied and sent about 
from one worker to another, so that results may be discussed 
at first-hand by various minds. 

The fact of largest philosophic interest which we owe to 
the spectroscope is the demonstration that the material of the 
solar system and of the universe as well is all the same. This 
had been long surmised ; obviously it could be only a con- 
jecture. Of the seventy odd elements known upon the earth, 
many show their characteristic lines in the spectrum of the 
sun. Not all ; and this has led to the idea that perhaps in 
the enormous temperatures of the sun our so-called elementary 
atoms are decomposed, disassociated into a comparatively few 
simpler forms. 

On the other hand, practically all of the solar lines could be 
accounted for. There were a few outstanding. They seemed 
unmistakably to indicate the existence of substances which no 
terrestrial chemist had ever seen. It is the essence of true theory 
that it shall, if need be, afford the basis of prediction. Spite of 
all the bizarre tracings with which he had to deal, the spectro- 
scopist did not hesitate. He announced new elements, gave 
them a name; he even hazarded a guess at their nature and 
their place in the chemic scale. 

So commonplace has all this become that it does not now 
seem bold ; quite the contrary. So closely interlinked are the 
physical investigations of to-day that what once seemed daring 
now appears merely a necessary consequence. It is the difference 
of the times. The predictions of the spectroscopist, it hardly 
needs be said, were subsequently verified, most notably by the 
discovery of the hypothetical element, helium, which does not 
belong to the sun alone, but to the earth as well. 

As the study advanced it became further evident that the 
spacing of the spectral lines is influenced by the temperature 
of the body from which the light comes ; if it be a gas, it is 
influenced by the pressure. In following out these and similar 



SPECTROSCOPE AND STUFF OF COSMOS 349 

clues, a new study came into being, that of solar physics. 
To-day we know more of the constitution, the temperature, and 
physical characteristics of a body ninety millions of miles away, 
and for ever inaccessible to man, than our forefathers three or 
four generations ago knew of the earth itself. Not merely this, 
but the spectroscope has reached out to tell the same story of 
the stars ; to-day the stellar bodies are divided according to 
their apparent temperature into different types — solar or yellow 
stars like our sun ; white or bluish stars like the great Dog-star, 
Vega, and others ; red suns like the bright star of the constella- 
tion of Hercules ; the subdivision is often carried much further. 

From out of solar physics has grown a yet broader study, 
that of stellar, or, if one prefers, of cosmic physics. Amid the 
multiplied interests of man there are surely none more distantly 
removed from his primitive pre-occupations for food and shelter 
than this. 

But the revelations of the spectroscope were not to stop 
with chemical and physical conditions. By an extraordinary 
circumstance, grounded in the very nature of light itself, it 
was to do more ; it was to prove an independent method of 
determining solar motion. 

There is much in the economy of science that resembles 
that of our workaday and business life. Very often it has 
happened that a loan of fact or theory from one branch of 
scientific investigation has later been returned with heavy 
interest. This was true in the present instance. It was the 
motion of the earth which first revealed the finite velocity of 
light. Later, as we have seen, this was turned about in ex- 
planation of the annual aberration of the stars. The return 
went further. 

If light be a form of wave motion, it follows that if the body 
which sets up these light waves be itself in motion, in sufficient 
velocity, this would occasion some disturbance in the behaviour 
of the light it transmits. You find a familiar analogy in sound. 
If while an express train is travelling at a high rate of speed 
the engineer blows his whistle continuously, this will seem to 
cause a change of pitch in the sound, accordingly as the train 
is travelling towards or away from a bystander. The fact is 
one of everyday experience. 

The case with light is a little different. Not only does it 



350 THE WORLD MACHINE 

travel at nearly a thousand times the velocity of sound, but 
its vibrations are crosswise to the line in which it travels. The 
motion of the source of light does not occasion a change of 
pitch — that is to say, of the light colour — but this movement 
is disclosed by a slight displacement in the position of the lines 
of the spectrum. 

The placing of the lines is determined by the wave-lengths 
of the different rays. If the source of light be approaching, 
the waves will be crowded a little closer together, with the result 
that the lines will be pushed up a little farther towards the 
violet end of the spectrum. Conversely, if the source of light 
is flying away from us, with suffiicient speed, the wave-lengths 
will be drawn out a little, the spectral lines will be displaced 
slightly towards the red end. By a marvellous refinement of 
measurement, this displacement can be utilised to reckon the 
speeds of stars moving directly in the line of sight — that is to say, 
which have a motion radial to that of the earth and the sun. 

This is accomplished by means of photography. If the 
spectrum of a moving star be registered upon a photographic 
plate, side by side with that of some source of light within the 
laboratory, whose lines exactly correspond with those of the 
star, the minute change of position due to the star's motion 
may be observed. 

By this means it has been possible, to some extent, to check 
the calculations as to the speed of the stars reckoned from the 
measures of parallax and of proper motion across the line of 
sight, or at least to render these calculations probable. If, for 
example, the speed of a number of stars of about equal magni- 
tude, and therefore probably of about the same distance from 
the earth, be computed first by the earlier method, then as 
many more by the spectral method, we may compare the 
averages. If they roughly agree, it is evident that in neither 
the one instance nor the other are we dealing with optical 
illusions. The chances against this concurrence being the result 
of a mere hazard has enormously increased as the number of 
motions thus reckoned increases, and with this increase the 
concurrence grows closer. Were it possible only to reckon the 
speed of the stars by means of their parallax, it might still be 
open to supposition that these computations were grounded 
upon some periodic disturbance like that of stellar aberration 
and nutation. Were the estimates grounded only upon the 



SPECTROSCOPE AND STUFF OF COSMOS 351 

displacement of the lines of the spectrum, the difficulties which 
the latter involves, the extraordinary delicacy of observation 
required, might equally leave the results open to doubt. Their 
substantial concurrence — that is, that the average speed of a 
hundred stars reckoned by the one method and a hundred more 
by the other, is not vastly different — brings a high degree of 
assurance. 

Some day or other the concurrence of these two methods 
may result in a reckoning yet more sublime — that is, the orbits 
of the stars. It is obvious at a glance that the spectrograph 
registers only the part of stellar motion that lies directly in the 
line of sight ; while, on the other hand, of proper motions we can 
know nothing, save that part of the motion which lies at right 
angles to the line of sight. If stars could be found having both 
a large radial motion and a large proper motion, likewise a 
measurable parallax, it would then be possible to estimate their 
actual speed, and to plot their paths as well. 

Obviously, however, such a condition could not obtain. If 
the apparent motion were large, the spectral displacement 
would be small, and vice versa, so the one or the other would be 
too minute for registry, unless perchance the speed were pro- 
digious and the placing of the star just right for such observa- 
tion. This is a problem of the future. It is clear that if a 
long series of observations could show, for example, that either 
the apparent or radial motion was growing greater or growing 
less, here at least would be a slender basis from which some 
sort of inference might be made. 

In following the disclosures of the spectroscope, especially 
in its amazing invasion of the invisible, we shall see that some 
stellar orbits have been found, not of the sort we have been 
considering, but quite another. Meanwhile, we are now in a 
position to sum up man's long endeavours to orient himself 
and his world amid the cloud of stars. The effort is considerable. 
The mind grasps with ineffectual fingers a vivid realisation 
of the teachings of the new time. Distances, figures, lose all 
meaning in their vastness. They leave only a blur. 
Let us try a little to sharpen the image. 



CHAPTER XXVIII 

OUR PLACE IN SPACE: THE PLURALITY OF 
WORLDS 



You tell us that Democritus says that there are a countless number 
of worlds, and that there are some which are not only so like one 
another, but so completely and absolutely equal in every point, that 
there is no difference whatever between them, and that they are 
quite innumerable ; and so also are men. 

Cicero, Academic Questions. 

The idea that there is but a single world in all infinitude would 
be as absurd as to suppose that a vast field had been formed to 
produce a single blade of wheat. 

Metrodorus, 3rd C. B.C. {De Placitis). 



CHAPTER XXVIIl 

OUR PLACE IN SPACE: THE PLURALITY OF 
WORLDS 

Blown about for days upon the tempest waters of the ocean, 
the first instinct of the mariner upon gaining some haven is to 
know, if he may, whither he has been tossed by the sport of 
the elements. If it be an unknown, uninhabited land, he will 
endeavour by the aid of the stars to fix its point upon the map. 
If it have there no place and its contours reach beyond the eye, 
his unconquerable ambition will be to know what is its extent — 
what is its shape. 

The position of man, tossed by the sport of chance upon 
our little earth, is much the same. From the earliest period 
he has sought — for a long time vainly — to gain some clue as 
to his latitude and longitude in space ; let us say, also, the 
extent of space itself. The ideas of the ancients could necessarily 
have been but of the crudest. Their whole knowledge of the 
earth, as we have seen, extended not much beyond the confines 
of a territory about the length and breadth of the United 
States. 

Within four hundred years we know how vastly this has 
changed, but the extent of the change is less easy to realise. 
Save for a few who interest themselves with the problems and 
the reports of the astronomers, not many, perhaps, have any 
vivid presentation of the reality. Perhaps we may reach this by 
a process of summation. Starting from familiar facts, from 
familiar distances, we may rise step by step, perhaps, to some 
vague conception of the cosmos in which we move. 

The longest voyage ever taken by the ancients was probably 
the circumnavigation of Africa, five or six hundred years before 
our era. It was rarely repeated. In general, the extreme 
extent of the Mediterranean and the Black Sea and along the 
western coast as far as Ultima Thule, was the utmost reach 



356 THE WORLD MACHINE 

of their more than ordinary voyages ; let us say, twenty-five 
hundred miles. 

When Sebastian de Elcano entered the harbour of San Lucar, 
in the month of September 1522, with the ships of the ill-fated 
Magalhaens, he had accomplished a voyage of between 30,000 
and 40,000 miles ; his armorial bearings carried a globe with 
the inscription, ''Primus circum dedisti me'' The ranges of the 
earth which men would now undertake to span had been multi- 
plied ten or a dozen times. 

The circumferenoe of the earth is roughly 25,000 miles. 
Could we leave the earth and voyage in space, the first object 
with which we might meet, barring a chance swarm of whizzing 
meteorites, would be the moon. It lies at very near ten girdles 
of the earth — that is to say, 240,000 miles. He who first 
measured the distance to the moon covered a space, then, some- 
thing like a hundred times the longest voyage which had yet 
been made by man. 

After that, space is a blank for a long way. Could we 
journey on from the moon, the first foothold we might gain, 
the hundreds of little asteroids disregarded, would be, were its 
position right, the planet Venus. The most brilliant object of 
the moonless night is, as we know now, about the same dimen- 
sions as the earth, surrounded doubtless with a dense atmos- 
phere, and perchance as likely to be peopled with intelligent 
beings as any other of the planets. Its distance from the 
earth at its nearest approach is about one hundred times the 
distance of the moon — that is to say, about twenty-five million 
miles. A spin to Hesperus, therefore, would, under the most 
favourable circumstances, involve a journey a thousand times 
longer than a trip around the globe. A voyage to Mars would, 
at the nearest, be one-third farther. 

The sun is at about four times the distance of Venus at its 
nearest approach — that is to say, roughly, four hundred times 
the distance of the moon ; roughly, four thousand circumferences 
of the earth. This is about ninety-three million miles. In the 
antique illustration of the railway train, a flying express which 
would carry the traveller from New York to San Francisco in 
two days would bring him to the sun in two hundred years. 
Were some solar Krakatoa to explode, we might see the effects 
eight minutes after ; but the report, did sound carry so far, 
would not be heard until fourteen years later. 



OUR PLACE IN SPACE 357 

Our little earth turns, of course, very near the sun ; it is one 
of the innermost of the planets. Jupiter is five times as far. 
Within the planetary scheme the remotest object which we may 
see with the naked eye is Saturn with his rings ; he is distant 
about ten times the way of the sun. The telescope brings within 
our view Neptune three times farther still. This, the outermost 
reach of the system, so far as we know it, lies at consider- 
ably more than a hundred thousand times a girdle of the 
earth, considerably more than a million times the width of the 
Atlantic, a little under twenty-eight hundred million miles. To 
skirt the rim of this system, Neptune, travelling at 200 miles 
per minute, requires 165 of our earthly years. 

Could we set out from this rim for a journey through space, 
so far as we know the first stopping-place which we might 
gain would be the alpha star of the constellation of the Centaur. 
It is something like nine thousand times the distance of Neptune 
— that is to say, about two hundred and seventy-seven thou- 
sand times the distance of the sun. To cross the intervening 
emptiness, could we travel at the speed of light, would require 
close to four and a half years ; at the speed of an express train, 
one million two hundred and fifty thousand years. 

The brilliant Dog-star lies apparently twice farther still — 
that is to say, at eight or nine light-years from our solar system. 
The Pole-star is something like forty light-years. These are 
among the nearest of the suns. 

With present-day micrometric methods, and still more by 
means of the photographic plate, it is possible to reduce the 
limits of error in measures of parallax to between o.oi and 0.02 
of a second of arc. As the accepted parallax of alpha Centauri 
is about I, or 0.75 of a second, it will be seen that there is Httle 
likelihood that further advances will seriously change our ideas 
as to the distance of the nearer stars. 

In all, measures of parallax have been effected with reason- 
able accuracy upon sixty to a hundred suns, and the number 
is growing steadily. But this, in the face of fifty millions 
or more which the gigantic telescopes of the present day will 
disclose, seems an absurdly small number ; it might readily 
yield the inference that their distance is for the most part 
so great that it would be hopeless ever to dream of trying 
to fix our place in cosmos. The easy conclusion would be 
that, so far as any human means of observation will ever 



358 THE WORLD MACHINE 

reach, the extent of the starry universe is an impenetrable 
enigma. 

This may well be ; but restless minds have not hesitated 
to attempt a guess. One is based upon the fact that we cannot 
as yet be certain that light is in any way absorbed in passing 
through empty space. It is an old remark that if it is not, 
and the number of stars is infinite, the heavens would be ablaze 
with light night and day, with a marvellous white light at that ; 
it would give to the disk of our sun the appearance of a sickly 
yellow. 

Nothing of the sort exists, and one inference we might draw 
would be that the number of the stars is finite. The explana- 
tion may be quite otherwise. Space, as we shaU see, holds 
more things than was imagined. The light of the stars may be 
cut off or dimmed in several ways. If it should turn out that 
it is not, in a vague way the number of the suns would be 
measurable ; and there has been more than one attempt in 
this way to indicate the limits within which their number must 
lie. One of these is based upon the amount of star-light which 
reaches us. 

Even in the old Alexandrian days, Hipparchus had adopted 
a method of classifying the stars according to their apparent 
brightness. Thus the Dog-star, Arcturus, Vega, and their Uke, 
were said to be of the first "magnitude" ; those a Uttle fainter, 
like the Pole-star, the " pointers " of the Dipper, of the second; 
and so on. AU that are visible to the naked eye were classed 
in six such divisions ; the faintest of them were broadly grouped 
in the sixth magnitude. With the invention of the telescope 
this method of classification has been carried out to the seven- 
teenth and eighteenth magnitude. It was noted that, roughly 
speaking, the number of stars catalogued in each order of mag- 
nitude was about three times that of the next. Calculating 
as nearly as he might the total intensity of star-light, the 
French astronomer I'Hermite endeavoured to estimate the 
number of suns which would be required to shed the fight they 
do. He fixed the outside limit of the possible number at 66,000 
millions. If star-light reaches us integrally and undimmed, this 
limit is certainly far outside of the reahty. 

A very ingenious method of attacking the problem in another 
way was worked out by the distinguished American astronomer, 



OUR PLACE IN SPACE 359 

Simon Newcomb. His idea in brief was this : within a radius 
of 400,000 times the distance of the sun from the earth there 
seems to be but one sun outside our own, the alpha Centauri 
noted above. If the stars were sown with some evenness in 
space, it would follow that the number of stars within a sheU 
of twice this radius would be the cube of this number — that is 
to say, eight. In a shell three times this unit of diameter there 
would be twenty-seven, and so on, the number increasing always 
with the cube of the diameter. The data at present available 
for such a calculation are as yet meagre enough; neverthe- 
less, in a way, the number observed agrees surprisingly with 
the number calculated. Moreover, it is possible to check the 
figures, in a way, from the measures of the proper motion of 
the stars. It is obvious that on the average the stars nearest 
to us wiU show the greatest annual change of position, and this 
gives a second but very crude method of calculating their 
number and distance. 

Putting these results together, Newcomb comes to the con- 
clusion that five hundred such concentric shells would include 
all of the stars visible to us by telescopic or photographic means. 
This would give, on the supposition of a perfectly even dis- 
tribution, something like 125,000,000 suns. It would mean a 
stellar universe thirty-three hundred light-years from one 
boundary to the other. But even conceiving that result is too 
small, merely doubling this diameter would give a total of 
eight times as many stars — that is to say, 1000 millions in all. 
The number is vast, but there is little or nothing to make it 
improbable. We may go further yet ; we may take the out- 
side limit set by I'Hermite — that is to say, 66,000 millions. This, 
on the same theory of even distribution, would require a universe 
five to six thousand times the space to the nearest sun — let us 
say, roundly, a universe with a diameter of around 25,000 light- 
years. 

Picture it, see it, realise it, who can ! 

It might seem as if we had here reached out far beyond the 
powers of the telescope, and yet this is in no wise certain. 
It was the calculation of Herschel that his twenty-foot reflector 
would penetrate — that is, reveal the existence of a star — nine 
hundred times the distance of Sirius, and that his forty-foot 
reflector would penetrate twenty-eight hundred times the dis- 



36o THE WORLD MACHINE 

tance. The actual ranges of the stars were, of course, not 
known to him ; but he seems to have made a splendid guess. 
According to present-day photometric methods, a star of the 
first magnitude sheds about a hundred times the light of a sixth 
magnitude, and so on, so that a star of the sixteenth magnitude 
sends only one-millionth as much light. So far as we now know, 
the brilliancy of a star varies evenly and inversely as the square 
of the distance. If this were strictly true, on the average, 
therefore, a sixteenth magnitude star would be about a thousand 
times as far away as one of the first. 

Herschel's forty-foot reflector, with an aperture of four feet, 
showed stars up to the seventeenth or eighteenth magnitude 
of our present-day classifications. 

There are twenty or twenty-one stars in the heavens accounted 
of the first " magnitude." The parallax of three-fourths of 
these has been fairly determined. With one exception, they 
are all under fifty light-years. Arcturus comes out at between 
two and three times this distance. The average of these known 
stars would fix the mean distance of first magnitude luminaries 
at about twenty-two light-years, or very evenly five times the 
distance of the nearest one we know of. This is more than one 
million times the space between the earth and the sun— that 
is, ninety-three million million miles. 

But there are at least three of the first magnitude stars 
whose parallax evades our present resources. Present methods 
would certainly disclose the shift of a star thirty or forty times 
the nearest, so that each of these three — Canopus, Rigel, and 
Deneb — must be considerably more than this. Sir David GiU 
considers that present limits of error will not permit us to suppose 
that Canopus is nearer than two hundred and ninety-six light- 
years. The fact that Rigel has practically no apparent motion 
seems to fix it at a still greater distance, and Deneb may not 
be much less. If we set the average of these three at three 
hundred light-years, this would raise the average for all of the first 
magnitude stars to above sixty light-years. We may conclude 
that the mean distance is somewhere between these upper and 
lower limits. It cannot be less, and it is probably not much more. 

Merely to fix our ideas of this distance, it may be noted 
that our shining sun would be of the first magnitude only within 
five or six Hght-years, and it would quite cease to be visible 
to the naked eye at much beyond thirty light-years. 



OUR PLACE IN SPACE 361 

All this would seem to indicate an average distance for six- 
teenth and seventeenth magnitude stars as somewhere from 
twenty to sixty thousand light-years ; the number is purposely 
stated very vaguely, because of a possible absorption of light 
through very long spaces. This appears to be the present limit 
of telescopic visibility. 

The present calculated distance of Sirius is somewhat under 
ten light-years (8.6 is the latest estimate). Herschel's figure, 
therefore, was not far out of the way if we set this distance at 
ten light-years. It is possible, though by no means certain, 
that we can see somewhat farther even than he supposed. 

If the solar system were situated an5rwhere near the centre 
of the stellar universe, as some recent fanciful philosophies of 
creation suppose, then of course our telescopes would be able 
to sweep across a cosmos of twice these computed dimensions, 
or of from fifty to a hundred thousand light-years. There is 
little reason to suppose, however, that we are at the centre of 
any system or anywhere near it. But even thirty thousand or 
fifty thousand light-years would mean a universe several times 
more vast than the utmost limit conjectured by FHermite. 
And the figure of FHermite was based upon the idea that the 
total light of the stars was equal to about one-tenth full moon- 
light. More recent and more accurate calculations seem to 
indicate that it is not much more than one-sixtieth full moon- 
light. In a word, I'Hermite's estimate may have been five or 
six times too high. So, if we could rely in any way upon our 
present assumptions, we might infer that the present powers 
of the telescope would reveal the existence of a universe perhaps 
a hundred times more vast than any which can be accounted 
for now from measures of light, or than Newcomb deems pro- 
bable from the methods employed by him. 

It is obvious that we can know nothing of the real distance 
of the farther stars until the question of the absorption of light 
is settled. Of course, if there is the slightest dimming of the 
light, the boundaries of the universe will be to us forever un- 
known. Presumptuous in the last degree is it, therefore, to 
attempt to fix the position of the solar system in space. A 
microbe upon the surface of a microscopic drop of mist in a fog 
covering the Atlantic Ocean would not be more hopelessly 
situated in his endeavours to discover his whereabouts. 

In the days to come, when the parallaxes of some thousands 



362 THE WORLD MACHINE 

of stars are known, we shall be a little better off. Then it will 
be possible to gain some idea of average star spacing, and we 
shall be able to fix the position of the sun, probably, with re- 
ference to the brighter and nearer stars. It is quite possible 
that we have much nearer neighbours, for example, than alpha 
Centauri. The analogy of the planets points to such a con- 
clusion. Uranus was discovered before any of the five hundred 
asteroids, and even Neptune before the most of them ; and 
the asteroids are on the average ten or twelve times nearer 
than the outer planet. 

Following the same analogy, it is likely that these more 
neighbourly suns or sunlets would be very much smaller than the 
star of the Centaur — that is, smaller than our own sun. For 
anything we now know, there is no reason to suppose that they 
may not vary as greatly in size as, let us say, the asteroids 
from Jupiter. There may be blazing suns no larger than the 
earth. On the other hand, between our own system and the 
Centaur there may be dark bodies vastly larger than our sun. 
They could scarcely be known to us save by their gravitational 
pull. For aught we now know, some of these dark bodies might 
be our nearest neighbours. If they had not been extinct too 
long, it would be very curious to visit them and examine, so 
far as we might, the ruins of extinct civilisations on their planets. 
Of course, the present chances of escape from our own system 
are exceedingly slight. But the advance in our physical know- 
ledge within the last two or three hundred years is probably 
but the merest beginning. He would be a blind man who would 
assert that such an escape is forever an impossibility. 

The conclusion of present-day computation is that the suns 
are numbered by the thousands of millions ; planets and dark 
stars probably by hundreds of thousands of millions. The dis- 
tribution would involve a corresponding vastity of space. 

There is no great interest in mere numbers, however pro- 
digious they may be ; but from out this computation of a 
seeming endless welter of blazing suns, at least one curious 
inference may be drawn — that is, the probably colossal number 
of inhabitable worlds. Our solar system contains at least nine 
bodies, ranging in size from Jupiter to the moon, which at some 
stage or other of their evolution might present a theatre for life. 
It now seems indubitable that the stuff of the universe is all the 



OUR PLACE IN SPACE 363 

same. If it had not been so in the beginning, we shall see 
that there is reason to believe it would become so in the 
course of any extended period of existence. If the stuff is 
the same, doubtless the properties inherent to matter are the 
same. We may scarcely regard our solar system as unique. 
We are led almost irresistibly to conclude that we may have 
many similars throughout the concourse of worlds. 

Let us conceive for a moment that there are in the sky no 
more, or that we shall never know of any more, than say a billion 
suns — a thousand millions. If our solar system be anything of 
an average type, this would mean five or ten billion planets 
that might be, at some period or other of their cooling-off, the 
seat of an animal population, perhaps of a civilisation and an 
intellectual development something akin to our own. The 
number is large. It can hardly excite in the mind more than 
a vacant mental stare. But consider the further inference. 
We have as yet, of course, only the vaguest estimates of the 
age of our planetary system, in the sense that it comprised 
definitely defined bodies. Present-day estimates range from 
twenty-five or fifty millions of years, up to several hundred. 
Let us take a figure far outside, and call it a thousand millions. 

Again, we may conceive that at some point or other over 
the earth our human civilisation has held at about its present 
level for ten or twenty thousand years. So far as primitive 
intellectual power is concerned, or in social organisation, in his 
pomps and ceremonies, his dress and his ways, man has pro- 
bably varied but little within this period. The time may be 
much longer. It is now clear that it was not less. 

Such minds as love to follow out calculations of probability 
wiU not fail to run forward to the conclusion. Let us say 
that the civilised life of mankind represents a hundred- 
thousandth part of the conceivably habitable period of our 
solar system, in any portion of it, and assume this system to 
be a universal type. It follows that it would need but a universe 
of a hundred thousand suns to conceive that there is at least 
one other existing planet which has reached.a stage of evolution 
almost identically parallel to our own. If we may reckon with 
a thousand million suns, the chances are there may be ten 
thousand such parallel worlds. 

Even this number is still enormous. It is quite beyond 
the powers of the human mind vividly to picture the existence 



364 THE WORLD MACHINE 

of ten thousand vast globes like the earth, each with its many 
continents, its white and black and yellow races, its Seven 
Wonders, and a wearisome line of Alexanders and Caesars, of 
Tamerlanes and Kubla Khans. Let us then come a little closer, 
pursue our fancy further. 

Conceiving our civilisation as dating back ten thousand 
years, if there be ten thousand planets of about the same degree 
of mental development as earth's humankind, it follows that 
there is at least one wherein the concourse of human history 
might be exactly parallel to our own. Somewhere in the distant 
ways, we might imagine a planet which, like our own, has just 
attained to a knowledge and use of electricity, just found the 
means of lightening its burdens by the employment of steam, 
just developed the art of painting, just found its Beethoven 
and its Wagner, just begun to agree to settle the differences 
among peoples by compromise or by arbitration, instead of 
by appeal to the bludgeon or to the largest number of bullets 
and bombs and fools to shoot them. 

For that matter, the fanciful mind might even reflect upon 
an even closer possible parallelism, upon some planet distant 
so far that even the light of its central sun is shut from our 
eyes — a parallelism of each of our human lives. Even upon 
our own earth, it is only our lack of imagination, conditioned 
in the very narrow limits of human intercourse, that hinders 
us from realising that, among the billion or billion and a 
half of folk who tread this ancient earth, each one of us must 
have hundreds, and perhaps thousands, of alter egos. 

The human pattern is not so diverse. There are few among 
us who have known a hundred persons so closely and intimately 
as to penetrate the inner working of their lives. Even in a 
hundred we discover innumerable traits and actions close akin 
to our own. In a hundred thousand the parallelism would 
become closer. In fifteen hundred millions undoubtedly it 
would coincide in multiplied instances. Our human pride bids 
each of us deem that he is in some sense unique, and that 
he orders his life after an especial fashion of his own. Could 
we visualise the reality, we should discover that we are, each 
one of us, but one of a thousand or one of ten thousand whose 
ideas, ambitions, dreams, and daily lives are, in all essential 
ways, identical. 



OUR PLACE IN SPACE 365 

This evident parallelism of our earthly existence seems the 
counterpart of the larger parallelism of the cosmic organism. 
Imaginative minds have not hesitated to conceive of other 
inhabited planets within our solar system. Mars has been a 
favourite field of operations for novelists with ultramundane 
fancies ; Venus may possess physical conditions much closer to 
those which obtain upon the earth. It may be that both of 
them, possibly others still, possess life in some form. Circling 
the infinitude of suns there may be an infinitude of others. 

All the advance of physical knowledge has been, as it were, 
convergent rather than dispersive — that is, it tends always to 
reveal a single operative cause at work through a variety of 
phenomena. The analogy irresistibly suggests that if we ever 
attain to an extended knowledge of cosmos, it will be found 
to be relatively simple, following much the same course of 
development, and built on much the same pattern. 

The quantitive measure may vary vastly. There is nothing, 
for example, to forbid our believing that each of the five hundred 
asteroids known to us may not have been one day, or may 
not one day be, the theatre of life in some degree. There is 
nothing to forbid our believing that the sun itself may one 
day become habitable. We do not as yet know what are the 
relative probabilities in the approach of the suns — as to whether 
they shall collide or go spinning one about the other as a binary 
system, like unto those with which the heavens seem filled. 
The latter might be the fate of our sun, or it might become 
satellite to some vast luminary like Canopus. If in either 
instance it were supplied with an exterior source of heat and 
hght, life would undoubtedly develop at some stage or other 
of its cooling. 

If the density of the asteroids be something the same as 
that of the earth, it is evident that the pull of gravity at their 
surfaces would be twenty or thirty times less, even among the 
largest of them. If the sun in cooling reaches the same density 
— that is to say, is reduced to one-fourth its present volume — 
the pull of gravity at its surface would be fifty times or more 
that upon the earth. It is evident that within our own system 
the physical conditions for the development of life would be 
extremely diverse. A being the size of an average man set 
upon an asteroid might " weigh " six or eight pounds. This 
same body set upon the sun grown cold might weigh four tons. 



366 THE WORLD MACHINE 

It is evident that the jelly-Hke substance of which our bodies 
are composed would, under such pressures as this, be simply 
squashed. To sustain such a weight, beings would have to 
have bones and muscles of the tensile strength of steel. 

It is difficult to conceive of a colloidal aggregation with 
such powers as this. Hence it is difficult to imagine the forms 
which life would take on upon a planet of the dimensions of 
the sun. It is quite inconceivable when we think of a planet 
of the possible size of Canopus. Were it of equal density with 
the earth, the pull of gravitation would be 10,000 times that 
of terrestrial conditions. Under such a force, a bar of steel 
upon a support would bend like so much putty. But, however 
it might be, if life were possible at all, probably it would differ 
in no general way, would involve no radically diverse order of 
sensations, and hence intelligence, than that with which we are 
acquainted. 

Speculative minds which love large deductions will scarcely 
self-withhold from a fairly obvious inference. Life, sensations, 
passions, intelligence, are an evident condition or result of 
material organisation. Not unique upon our own planet, they 
are probably part of the universal order, if a universal order 
exists. This being so, it follows that the activities of life, the 
reflexes of our sensations, the impulses of our passions, the 
leadings of our intelligence, are aU a part of the cosmic order — 
that is to say, if it exist, of the cosmic machine. The supple 
movements of our bodies, the lifting of a hand, the turn of 
an eye, a given pain or pleasure, the sensations of a hurt, 
the joy of a lover's return, the promptings of avarice, the 
thirst for power, the passion of beauty, the visions of the 
prophets, the inductions of a Newton, the generalisations of a 
Spencer — all are a part of cosmic phenomena, and doubtlessly 
distributed with cosmic prodigality. Every thought, every idea, 
every rush of emotion, every flame of anger, every hidden wish, 
every heart-sickness, every little joy that we experience, we 
may conceive has its counterpart in hundreds, perhaps 
thousands, possibly millions, of similar beings with identical 
sensations and emotions, some separated from us by the width 
of a street, some by the distance of Cathay, some by spaces 
millions of times the distance of the sun. 

Phenomena so widespread can hardly be the result of in- 
dividual and diverse causes. We can only infer that our lives 



1 



OUR PLACE IN SPACE 367 

are as strictly conditioned and as strictly ordered as the march 
of the planets or the flash of a shooting-star in the skies. 

Let him who revels in the sense of his importance, or him 
who believes that in the face of the larger concourse of nature 
our human efforts are more potent than Joshua before the sun 
as it rose over Gibeon, observe a little the slow turning of the 
cosmic wheel. Let him learn that his delusions, like those of 
Joshua, are conditioned in his darkling ignorance and the 
childish simplicity of his mind. 

Mention has been frequent of the cosmic order and the 
cosmic structure — always, be it understood, with due recogni- 
tion of the present limitations of our knowledge. Within a 
few decades a new and larger chapter of astronomy has been 
opening that may wholly transform our ideas. Its very name 
is half a paradox ; it deals with worlds unseen, perhaps never 
to be known to us save as an inference. 

The wonder of the starry realms is not yet dead. 



CHAPTER XXIX 
THE ASTRONOMY OF THE INVISIBLE 



2 A 



The world in which we Uve and move 

Outlasts aversion, outlasts love, 

Outlasts each effort, interest, hope, 

Remorse, grief, joy ; — and were the scope 

Of these affections wider made, 

Man still would see, and see dismay'd, 

Beyond his passion's widest range. 

Far regions of eternal change. 

Nay, and since death, which wipes out man. 

Finds him with many an unsolved plan, 

With much unknown, and much untried. 

Wonder not dead, and thirst not dried, 

Still gazing on the ever full 

Eternal mundane spectacle — 

This world in which we draw our breath. 

In some sense, Fausta, outlasts death. 

Matthew Arnold, Resignation. 



CHAPTER XXIX 

THE ASTRONOMY OF THE INVISIBLE 

When the pattern of our solar system has been made out, it 
was the most natural thing in the world to suppose that count- 
less other systems were cut out more or less in the same fashion. 
The scheme was engagingly simple — a giant sun at the centre, 
with a gay retinue of little planets skimming round about his 
worshipful majesty and deriving from him their sustenance and 
the order of their lives. 

There came a rude jostle when the astronomers discovered 
that there might be systems with two huge suns. With minds 
attuned to a sense of unitary dominance, the " star " system, 
let us say, the idea of divided primacy seemed as incongruous 
as would a performance of Hamlet with two counterfeits of 
the melancholy Dane. But the fact could not be denied. 

Herschel had demonstrated that double-star systems actually 
exist. But little progress was made until the subject was taken 
up by the two great parallax hunters, Struve at Dorpat and 
Bessel at Konigsberg. It foUowed very naturally from their 
study of stellar distance, wherein the accurate determination 
of the position of a star was of fundamental importance. If 
through a period of years two carefully located stars were found 
to separate slightly, then draw together again, it was a fair 
inference that they were in reality revolving one around the 
other. It seems a slender thread to build upon. But such a 
quantity of evidence has come subsequently as to permit no 
question. 

Some of these double-star orbits, especially those surmised 
by Herschel, are so vast, they can as yet only be guessed at 
vaguely. Some twenty-eight or thirty are known with periods 
of less than a hundred years, and therefore with more or less 
certitude. 

It is a matter of very curious interest to note that in two 
of the best known of these revolving pairs the companion sun 



372 THE WORLD MACHINE 

was long invisible to the eye. In each case its presence had 
been divined, its position predicted, estimations of its mass 
been made, before actual visual observations had confirmed 
the fact. 

The earliest of these predictions was that of Bessel re- 
garding the companion of great Sirius. It could have been only 
a keen, and in some sense poetic, imagination which inspired 
this great astronomer to his daring prophecy. " The astro- 
nomy of the future," he said, " wiU be the astronomy of 
the invisible." The embracing mind of Laplace had caught an 
inkling of the same truth. Bessel was bolder. It was he who 
first determined absolutely the monstrous distance of the stars, 
the first who showed that Huyghens' estimate, vast as it was, 
might be multiplied ten and twenty times before we approach 
reality. For aught that any human eye could see, the space 
between was void. 

But in 1844 his observations of Sirius led him to announce 
the probable existence of a dark companion. He came to the 
same conclusion regarding the very brilliant star Procyon, in 
the neighbouring constellation of the Little Dog. Their times 
of revolution he set at about half a century. Twenty years 
after, his predictions were verified in a curious way. 

The American firm of telescope builders, Alvan Clark & Sons, 
were finishing a wonderful new refractor, and the younger 
member of the firm turned it upon Sirius to test its powers. 
He exclaimed to his father that the star appeared to have a 
companion. He knew nothing then of BesseFs work, nor the 
later and more precise calculations of other investigators, who 
had to all intents demonstrated that the companion must be 
there. But repeated observation left no doubt. 

The companion was most remarkable for its dimness ; its 
giant partner gives perhaps ten thousand times as much light. 
It appears to be about half as big as Sirius — that is, perhaps 
twelve or fifteen times the bulk of our sun. It is evident, then, 
that the companion does not shine merely by the reflected Hght 
of the glowing Dog-star, for they appear to be separated as 
widely as Uranus and our sun. The diameter of the com- 
panion, therefore, would have to be something enormous, ap- 
proaching the size of Canopus perhaps, did it possess no lumi- 
nosity of its own. The inference, therefore, is that it is a dark 
sun, one of the dying embers of the flaming universe. 



THE ASTRONOMY OF THE INVISIBLE 373 

Of especial interest to us is the fact that the nearest of 
the stars hkewise forms one of these binary systems. Alpha 
Centauri has a double ; their period of revolution, as estimated 
by See, is eighty-nine years. They are separated apparently 
about as widely as Sirius and its companion, and their combined 
mass is computed at about double that of our sun's. When 
we put with this Sir David GiU's conclusions, on other grounds, 
that alpha Centauri is almost the duplicate of our sun in tem- 
perature, density, and the like, we may conclude that the com- 
panion is of about the same density and only a little less 
luminous. 

Of the six binary systems of which both the orbit and parallax 
are known, and from which therefore their mutual distances 
may be estimated, there is only one in which the space of separa- 
tion seems greater than the distance of Neptune from the sun. 
In one of the nearest, and therefore most certainly observable, 
of the six, that of Procyon, the distance of its companion is 
apparently not more than ten times the earth's distance from 
the sun — that is, about the distance of Saturn. 

When now we compare these apparently well-fixed distances 
with the periods of their revolution, we gain some idea of their 
speed. It is not very different from that of the planets. The 
period of Saturn is twenty-nine and a half years ; that of the 
companion of Procyon is forty years. The companion of Sirius, 
at about the distance of Uranus, completes its circuit in fifty- 
two years, where Uranus takes over eighty. It is therefore 
moving about twice as fast. The companion of alpha Centauri, 
at about the same distance, moves at nearly the same speed 
as the planet. 

But it is from the spectroscope that the most interesting 
discoveries of binary systems have come. It is easy to per- 
ceive the mode. If the spectroscope can disclose the radial 
motions of the stars, it would foUow that it ought equally to 
disclose the periods of revolution of a binary system, provided 
their motion is sufficiently rapid. If the system were at rest, 
compared with our own, or moving more or less at right angles 
to the line of sight, the backward and forward motion the two 
stars present to an observer would be represented in their 
spectra by a backward and forward motion of the bright and 
dark lines. If the system were moving within the line of sight, 
the mutual revolutions of its suns would be revealed by a constant 



374 THE WORLD MACHINE 

alteration in the apparent speed, and by a definite periodicity of 
that alteration. For example, if such a binary were approaching 
or receding from our sun at, say, a speed of a hundred kilometres 
per second, and at the same time were whirling about a centre 
in an orbital velocity of about the same rate, the lines of the 
spectrum would shift according as the one star or the other 
was coming towards us or receding from us in its own orbit, 
with a regularly varying rate, at one time standing still, 
then moving at a rate indicating twice the speed of the actual 
translatory motion of the double system. 

Precisely these conditions were disclosed in the same year 
of 1889, by Vogel of Berlin and Pickering of Harvard. Since 
this time the number of these " spectroscopic binaries " has 
grown rapidly. At the present time more than sixty such 
systems are listed, and their periods fixed. It is easy to see 
that it would be difficult, if not impossible, to discover by means 
of the shifting of the spectral lines a system of long period. 
It follows, therefore, that there is a very marked contrast in 
the period of the spectroscopic binaries and those observed by 
means of actual change of position. With possibly a single ex- 
ception, no double system has been revealed by means of actual 
shift of position of less period than eleven years. On the other 
hand, no spectroscopic binary has been noted with a longer 
period than about three years. They range from this down to 
about a single earthly day. 

We cannot imagine the arrangement of these short-period 
binaries save in one of two ways : either that their orbital 
velocity is enormous, or else that they are relatively very close 
together. But their orbital velocity is known by the same 
means which disclosed the fact that they are binaries. The 
greatest speeds computed for any of the short-period systems 
is from 250 to 300 kilometres per second. This is eight or ten 
times the speed of any planet in our system. It is still quite 
insufficient to explain the extreme rapidity of their revolutions. 
Moreover, the most of them are very much less than this. The 
Pole-star, for example, is a double star, with a period of four 
days, and the computed orbital velocity of its components is 
only three kilometres per second. This is very slow. 

We are forced to conclude, therefore, that in many, if not 
in most, of these double systems, the two suns are very much 
closer to each other than any of the planets to our sun. For 



I 



THE ASTRONOMY OF THE INVISIBLE 375 

example, the period of Mercury is eighty-eight days, and its 
orbital motion is nearly thirty miles a second. It is the fastest 
member of our system. If the twin stars of Polaris are travel- 
ling at an average speed of only a mile or two per second and 
encompass their mutual revolutions in four days, they cannot 
be separated by more than a small fraction of the distance 
of Mercury from the sun. 

These revelations bear with them many interesting implica- 
tions. The detection of a binary system either by means of 
the spectroscope or by measures of actual displacement, is a 
matter of the most delicate observation. The shifting of the 
lines in the spectral image is exceedingly minute ; the inferences 
one may draw are complicated by many physical problems, 
each of which may introduce a possible error. It is obvious that 
each system must be treated by itself — one does not lead to 
another. All this takes time. 

On the other hand, the actual displacement of the double 
stars from their observed positions is measured for the most 
part by hundreds of seconds of arc, and we have already seen 
what accuracy these micrometric measures involve. Sometimes 
the series of observations must extend over half a century or 
more before any reasonable inference may be drawn. Here 
again the chances of error are great, and progress is necessarily 
slow. 

If, in spite of all this, a little more than a dozen years has 
sufficed to reveal more than sixty spectroscopic binaries, the 
obvious inference is that their number is enormous. Let us 
supplement this with the fact that out of the comparatively 
small number of stars whose positions have been determined 
with very great accuracy, at least two hundred and fifty are 
known to be double systems, with fifty or sixty of their orbits 
measured from their displacements. Add to this that per- 
haps ten thousand stars are known, situated so nearly together 
that for the most part they can only be resolved into two by 
means of telescopes of the highest powers of magnification — 
double stars in the Herschelian sense. One might almost con- 
clude from this that the double-star system was the general 
pattern of the universal arrangement, and that our solar system, 
so far from being the type, was relatively unique. One 
might go further, and conclude that a companion of our sun 



376 THE WORLD MACHINE 

would eventually be found. This is always possible ; but as 
we have seen, it is highly improbable. 

So perhaps is the other inference that the universe is made 
up mainly of double suns. The marvellous progress in late 
years in photography of the nebulae seems to have spread before 
our eyes the general course of stellar evolution. The images 
which have been obtained of revolving nebulae present neither 
the general type of a disk with a single centre of condensation, 
nor that of a double centre, such as the binary arrangement 
would suggest. Rather we find all types ; sometimes a single 
central nucleus, sometimes a pair of nuclei, sometimes three 
or four. 

For a long time we have known of stars that seem to be 
triple, or even multiple. The larger part of these doubtless 
are merely optically triple or multiple, and have no physical 
connection. But we may infer that some of them do constitute 
a system, and the photographic plate seems to reveal a quantity 
of these triple and multiple systems in the actual process of 
their evolution. This suggests readily enough that there is no 
single type, no common mould, but that could we journey 
through the stars, we should find a considerable variety, some 
of them alone in solitary grandeur like our sun, some of them 
sharing their thrones with a companion sun, others with dark 
companions. There may be triumvirates and decemvirs, and, 
for aught that we now know, conceivably centos and cinquecentos 
— that is to say, twins and triads and clusters and swarms. 

Of course, if there be aught in the idea of stellar evolution 
and the nebular theory, and we have no other theory of creation 
worth considering, there may have been a time when our own 
system presented the appearance of a cluster of suns. The com- 
panions of the central mass, however, are so insignificant, 
even the greatest of them, Jupiter and Saturn, that they would 
be all but invisible at the distance of the nearest known star. 
But the telescope has revealed, as the photographs of nebulae 
have suggested, that this partition of the mass of matter within 
a system is not always so dismeasured. The separating masses 
may be more nearly equal. 

We meet here with a perplexing problem. The fact that our 
own sj^stem is made up of more than five hundred individual 
bodies, the most of them, so far as we can see, in stable motion, 
readily suggests that other flaming suns are likewise companioned, 



THE ASTRONOMY OF THE INVISIBLE 377 

perhaps not always so numerously, perhaps sometimes more 
so. But with two central masses, each of the proportions, let 
us say, of our sun to the rest of the planets, it is difficult to 
conceive how such a system could long subsist. If they were 
spaced as closely as the two components of the Pole-star appear 
to be, for example, the problem would be relatively simple. 
Then their satellites might revolve around the common centre 
of gravity ; but obviously with a somewhat perturbed motion. 

But if they were as widely separated as Neptune and the 
sun, as some of the binaries appear to be, probably each of the 
pair would have its satellites. If these latter were at any con- 
siderable distance, like Jupiter, they would be most curiously 
pulled about in their orbits when they came in conjunction 
between the pair of suns. Life on such planets, if they 
exist, would be a topsy-turvy affair. When in conjunction, day 
would be of course continuous, ocean tides would probably 
be enormous, the course of the seasons would doubtless be quite 
broken up — certainly if the axes of the planets were inclined 
to the plane of the ecliptic like our own. Their inhabitants 
would experience the most violent changes of temperature, with 
consequent storms and a general derangement of physical 
conditions. 

Altogether, when we try to project our own little scheme of 
things into the general order of the universe, we are hopelessly 
estopped by the very beginnings of our knowledge of stellar 
arrangements. In another two or three centuries, doubtless, the 
case will be different and our knowledge considerable. 

In a general way, our representation of our immediate 
planetary system is complete. We cannot conceive it as very 
materially altered by any subsequent discovery. We know the 
distance and size of the sun, the planets, their satellites, and 
this so accurately and surely that " astronomical knowledge " 
has become the synonym for fixity and certitude. 

Our knowledge of the solar system represents an effort of 
the human mind extending through several thousand years. 
The larger and more definite part of this knowledge has all 
come within three centuries, the last details within fifty or 
sixty years. 

Accurate star-knowledge dates from Bradley and Herschel — 
that is to say, from a little more than a century and a half — 
and it is concerned with motions for the most part less per- 



378 THE WORLD MACHINE 

ceptible in a year than planetary motions in a day, with distances 
in which the prodigious remoteness of the sun becomes a unit 
of measure. The perfected telescope is not a century old, the 
spectroscope is not a half-century, and the application of photo- 
graphy is hardly a quarter of a century. In another three 
hundred years we may know a thousand or perhaps ten thou- 
sand times as much about the stars and the universe they 
compose as we do now. 

The spectral image and the subtle movement of its cryptic 
lines have revealed to our wondering ken a considerable number 
of the stars as tumbling about each other in a sort of rollicking 
kirmess, furious as the wild romp portrayed by Rubens' ebullient 
sketch in the Louvre. It would be curious if it should stop 
here ; it does not. 

The development of our knowledge of binary systems has 
obviously lent a powerful support to the theory of stellar col- 
lisions ; and the importance of this is great. We shall see 
hereafter that our conceptions and theories of stellar evolution 
and devolution are pivoted upon the reality of this fact. 

It is in no wise probable that the generality of the binary 
systems came from any binary matrix. We need not conceive 
them as necessarily evolved from the same nebular mass. Pos- 
sibly much the larger part of them were as purely the result 
of chance, let us say, as the appearance of a shooting-star in 
our atmosphere. In the larger sense there is, to be sure, no 
chance anywhere. To the infinite eye, did any such exist, the 
flash of the shooting- star, the collision of suns, would all seem 
as definitely fixed and predictable as the rambles of a roulette 
ball. We can conceive of no such infinite eye. But in so far 
as our knowledge is real knowledge, the human mind ap- 
proaches, though at vast distance, to this infinite intelligence. It 
may be some hundreds of years, possibly a million, before 
the human mind attains such heights. Conceivably our orderly 
little system of planets might be disrupted, or life upon the 
earth become for one reason and another physically insupport- 
able, before the mental evolution of the race had proceeded 
so far. 

In our present ignorance we can only conceive the approach 
of suns, like that of the molecules of water vapour in the steam 
chest, as to all intents fortuitous. In the one instance as in 



THE ASTRONOMY OF THE INVISIBLE 379 

the other there is a chance formation of a double system, whose 
existence may be relatively that of a moment, or of an seon. 
The conception of the helter-skelter flight of the stars, com- 
bined with the extension of the law of attraction, long ago 
suggested that the number of such binary and multiple systems 
must be very great. This involved a corresponding, though 
lesser, number of actual collisions. In a very striking way 
has the spectroscope confirmed these conclusions. 

Long ago the sudden appearance of a very bright star in 
the skies obtained its due meed of wonder and surmise. The 
Star of Bethlehem may have been more or less of a myth. One 
of the best known was the famous star of Tycho. It was first 
seen on 7th November 1572. Four days later it had grown 
to the first magnitude. It continued to increase in brilliancy, 
finally rivalHng Venus at its brightest, and becoming visible 
in full daylight. A month later it had begun gradually to fade, 
and in the following May it had disappeared from view. The 
telescope was then, of course, unknown. 

This is the type of these apparitions. Formerly they were 
supposed to be very rare. Miss Gierke, in her System of the 
Stars, was able to list only ten which were known up to 
the end of the fifteenth century — that is, until the coming of 
the telescope. Not many more have been found since ; but 
it is notable that ten or twelve of these have come within 
the last century. One observer, Mrs. Fleming, has made the 
subject her speciality, and she already has eight to her credit. 

There is, of course, no reason to suppose that they have 
been any more frequent within the last twelve or fifteen years 
since Mrs. Fleming began, than in the twelve or fifteen years 
preceding, or than in thousands or miUions of years. The 
difference is simply due to perfected methods of observation. 
Doubtless if these methods could be still further refined, these 
conflagrations would be found to be daily and conceivably 
hourly happenings. We do not observe them simply because they 
are for the most part so remote that they do not strike the 
attention even of observers with telescopes of enormous power. 
For the most part actual visual observation is quite unable 
to cope with the problem, and resort is had, therefore, to star 
photographs and spectrographs. 

These new stars or novcB, as they have come to be called, 
seem to have a rather characteristic spectrum, so that when an 



38o THE WORLD MACHINE 

observer has become familiar with this especial spectral arrange- 
ment, he may be led to suspect the existence of a nova when 
it appears in his spectrographs. If then he possesses a series 
of photographs of the region, he may readily observe whether 
or no there be any star at this point which had been increasing 
in brilliancy. All this, it will be seen, is quite outside of the 
usual work of the observatory. It may be pursued as readily 
in the library, or floating around on a duck-pond, as on the top 
of Mount Hamilton, and resembles very much the ingenious 
method by which Mr. Berenson digs from obscurity unknown 
painters by means of the tell-tale eyes and ears which they 
have drawn. 

Could they be close regarded, the blazing up of these nova 
would doubtless be, in mere extent, the most impressive spec- 
tacle which the realms of nature afford. The most notable 
recorded since the days of Kepler was that observed by Dr. 
Anderson in February of 190 1, flashing out from amidst the 
constellation Perseus. It chanced that this very region had 
been photographed by the Harvard Observatory several times 
during the month of February, and up to two days before the 
star was noted by Dr. Anderson. So we happen to know 
that it must have risen from a star of below the twelfth magni- 
tude to a star of the first within about three days. It became 
the brightest star in the heavens, Sirius alone excepted. The 
difference of its light within these three days corresponded to 
an increase of twenty-five thousand fold. 

The apparition faded rapidly but fitfully, until it has be- 
come visible only as a little star of the twelfth or thirteenth 
magnitude. The most careful observations have failed to 
detect for it any parallax or proper motion, so that it is certainly 
not nearer than a hundred light-years — that is, ten times the 
distance of Sirius — and probably very much more. 

After the outbreak the star was found surrounded by a 
striking nebulosity. This it was possible to photograph, and 
likewise to make a measure of its apparent diameter. If it be 
distant no more than a hundred light-years, the extent of the 
nebula must be at least fourteen hundred times the diameter 
of the earth's orbit. Professor Young accounts this an under- 
estimate. 

Repeated photographing of the star brought to Ught an 
astounding and almost inexplicable phenomenon. It was ob- 



THE ASTRONOMY OF THE INVISIBLE 381 

served that there were in the nebula well-defined knots and 
streaks of condensation. These were estimated to be moving 
away from the star at such a speed that, if it were as near as 
alpha Centauri, would mean a velocity of more than two thou- 
sand miles per second. If the distance is fifty or a hundred 
times as great, the speed becomes comparable with that of light 
itself. The most plausible explanation of the phenomenon 
offered was that suggested by Kapteyn, that this motion of the 
knots and streaks was merely apparent and not an actual rush 
of masses of star matter. It represented simply a progressive 
illumination of spiral streams of nebulosity, advancing outwards 
with the speed of light. If this explanation is correct, the 
distance of the star would be about three hundred light-years, 
and its actual outburst occurred about the time that Columbus 
was discovering America. It follows from this estimate that 
the diameter of the resulting nebula was perhaps two or three 
hundred times that of the distance of Neptune from the sun. 

If our sun had been the body or one of the bodies involved, 
our earth would have been enveloped in a vast mass of nebulous 
matter, probably hot, irradiating the entire sky and abolishing 
night and day. Probably the heat would have been so great 
that every vestige of life would have been instantly shrivelled 
at the first onset of this flaming deluge ; the crust of the globe 
itself might have been melted, and the earth have returned 
to the primitive condition from which it sprang. 

It is by no means certain as yet that these stupendous out- 
bursts really represent starry collisions. For a little time the 
behaviour of their spectra seemed to negative this view. But 
the researches of Ebert of Munich made clear that the per- 
plexing contrariety of apparent motions was readily explicable 
on the theory of anomalous refraction. On the other hand, it 
is evident that the swift rush of a sun or dark body through 
a dense mass of nebula would produce the same spectacle. 
The number of nebulae we now know to be enormous. They 
may be counted by the hundreds of thousands, and their extent, 
even measured by sidereal standards, can only be regarded as 
something monstrous. 

Both explanations may turn out to be true. A variety of 
circumstances make it probable that actual collisions do take 
place, and with such frequency as to be quite unaccountable 
from any calculus of probabihty based upon our present ideas 



382 THE WORLD MACHINE 

of the spacing of the luminous suns. These probable collisions, 
combined with the evident number of binary systems, tend to 
confirm the conclusion we have reached upon other grounds, 
as to the enormous number of dark bodies. More than thirty 
years ago, and before the variety of evidence now at hand had 
been accumulated, Professor Johnstone Stoney, from a pro- 
found study of stellar phenomena, was led to say : — 

" If what I here venture as a surmise with respect to the 
cause of stellar heat and the origin of double stars, is what 
really takes place, we must conclude the sky to be peopled 
with countless hosts of dark bodies, so enormous that those 
which have met with such collisions as to render them now 
visibly incandescent must be comparatively few indeed." ^ 

The astronomy of the invisible, it will be perceived, is as 
yet in its infancy. There is already sufficient to indicate that 
its field is immense — that is to say, that the number of dark 
bodies probably far transcends the number of those which the 
telescope brings in view. In a sense this is yet a surmise. It 
is obvious that until the matter can be cleared up our know- 
ledge of the cosmos can at best be incomplete, our conjectures 
as to its form and structure but provisional. 

It is only very recently that this fact has become clear. In 
ignorance of it, the astronomers did not hesitate to build up 
vast systems which had little larger foundation perhaps than 
their own imaginations. It will perhaps be of interest, never- 
theless, to pass them in review, and endeavour to sift out any 
elements of truth they may contain. Possibly from the wreck 
of them we may gather some ideas. 

1 Proc. Royal Society, 1861-69. 



\ 



CHAPTER XXX 
THE STRUCTURE OF THE UNIVERSE 



Long before the discovery of the New World, it was believed that 
new lands in the far West might be seen from the shores of the 
Canaries and the Azores. These illusive images were owing not 
to any extraordinary refraction of the rays of light, but produced 
by an eager longing for the distant and the unattained. The 
philosophy of the Greeks, the physical views of the Middle Ages, 
and even those of a more recent period have been eminently 
imbued with the charm springing from similar illusive phantoms 
of the imagination. At the limits of circumscribed knowledge, 
as from some lofty island shore, the eye endeavours to penetrate 
to distant regions. The belief in the uncommon and the wonderful 
lends a definite outline to every manifestation of ideal creation ; 
and the realm of fancy — a fairyland of cosmological, geological 
and magnetic visions — becomes thus involuntarily blended with 
the domain of reality. 

Humboldt, Cosmos, 



CHAPTER XXX 

THE STRUCTURE OF THE UNIVERSE 

Looking up of a summer's night into the firmament with its 
countless silvered points of light, there seems little enough to 
suggest any idea of arrangement or order. For aught that the 
unaided eye might know, they might be merely incandescent 
bulbs stuck at random in the ceiling of the sky. For all we 
can see, they wheel together about the pivot star. 

In the beginnings of astronomy there seemed as little order 
or arrangement in the movements of the errant stars, the 
wanderers, the planets. They went in a zigzag aimlessness 
across the heavens, marching forwards and backwards in a 
bizarre fashion that was at first unaccountable enough. It 
was long centuries before men were able, from this apparent 
tangle, to reach the idea that the planets move in circles. When 
at last it was made clear that they do, the simplest arrange- 
ment that could be imagined for the unmoving stars was to 
suppose they were attached to a crystal sphere which enclosed 
space. This, as we know, is what the ancients did. 

Among the ancients there were a few, like Democritus, who 
could rise to more sublime conceptions ; there were very few. 
But when in our modern time the planetary arrangement had 
at last been solidly grounded, the question of the spacing of 
the stars came back again. 

Our human knowledge has often advanced through recourse 
to analogy. Vaguely we have come to perceive that the order 
of phenomena is relatively simple. In our ignorance we imagine 
more than is needful. The explanation of one narrow group 
of facts leads often to the enchainment of many. When, in 
the seventeenth century, the remoteness of the stars, or, in 
other words, the detachment of the solar system, had become 
clear, it was natural to think of our planetary arrangement as 
a microcosm which might be the mirror of the macrocosm. 

It is hard to say to whom the idea came first. The imper- 

385 2 B 



386 THE WORLD MACHINE 

severant Kepler speculated about it, as he did upon nearly 
everything else under the sun. Bruno, as we have seen, had 
revived the Democritan idea that the stars are blazing suns ; it 
lay but little further to suppose, as he did, that they have planets 
revolving in their train as does our own. It was this thought 
which inspired Fontenelle's brilliant volume on the PluraliU 
des Mondes. Before the century had ended, and when the gran- 
deur of our orb had been established beyond all cavil, Huyghens 
had boldly announced the possibility that there might be other 
suns as vast. Yet for his heresy he did not hang or burn. 

The same thought had come to Newton ; it is reflected in 
the pages of Milton too. But the first definite presentation 
of the idea that the stars might be arranged upon some definite 
system like unto our own, seems to have come from an obscure 
English schoolmaster, some time after all of these had passed 
to earth. This was Thomas Wright of Durham. His volume 
appeared in 1750, with a long-train title, as was the habit of 
the day : "An original Theory or New Hypothesis of the 
Universe, founded upon the Laws of Nature and solving by 
Mechanical Principles the General Phenomena of Visible 
Creation ; and particularly the Via Lactea." It was a godly 
book, and the author felt properly constrained, after the fashion 
of the time, to show that it tended towards the promotion of 
virtue and piety. He says : — 

" In a system naturally tending to propagate the Principles 
of Virtue, and vindicate the Laws of Providence, we may indeed 
say too little, but cannot surely say too much ; and to make 
any apology for a work of such nature, where the Glory of the 
Divine Being of course must be the principal object in view, 
would be too like rendering virtue accountable to vice for any 
author to expect to benefit by such an excuse." 

Thomas Wright was the author of the Grindstone Theory, 
which, amid many vicissitudes, has more or less held the field 
to the present time. His ideas were comprehensive. He com- 
puted that the Milky Way must contain at the very least three 
or four million stars, and he adds : — 

" When we consider them all as flaming suns, progenitors 
and primum mobiles of a still much greater number of peopled 
worlds, what less than Infinity can circumscribe them, less 
than an Eternity comprehend them, or less than Omniscience 
produce and support them, and where can our wonder cease ? " 



THE STRUCTURE OF THE UNIVERSE 387 

None the less he conceives the sidereal creation as finite, 
and he invites the reader to imagine a vast gulf or medium 
everywhere extended like a plane, and enclosed between two 
surfaces, the whole of it spaced with stars. To an eye situated 
anywhere near the middle point of this plane, it is evident that 
towards the poles there would be an apparent promiscuity ; 
but that looking across the plane in either direction the stars 
would seem crowded together, and thus might readily produce 
the appearance of the Milky Way. In other words, he con- 
ceived that the arrangement of the stars may be that of a huge 
heavily flattened globe, or, as we have since come to think 
of it, in the shape of a grindstone. He, of course, regarded 
the sun as the centre of this system ; from it proceeds " that 
mystic and paternal power productive of all life, light, and 
the infinity of things." 

These ideas of Wright were caught up by the young Kant, 
to form, as we shall trace hereafter, the basis of his cosmical 
theory. A few years later, and quite independently of either 
Wright or Kant, came the Cosmological Letters on the 
Arrangement of the World-Structure, from the pen of Johann 
Heinrich Lambert, contemporary worker in the fields of Laplace 
and Lagrange. It was beyond doubt a remarkable book. 
Lambert was at once a mathematician and a poet, with an 
imagination which outran that of all his predecessors. Even 
yet our knowledge is quite insufficient to estimate the value 
of his grandiose conception. It was that of a universe made 
up of wheels within wheels. His ideas might readily have been 
suggested by an attentive study of the arrangements of our 
system. He simply conceived it as the image of the whole. 
The beginning, that is, the first order, would be that of the 
planets with their satellites or moons. Next after this would be 
the sun with its planets. Our sun, with others like it, he 
imagined as turning about another centre, this in its turn, 
with others, around yet another ; and so on until the mind, 
reeling beneath the immensity of such conceptions, will no 
further go. 

Just as in each of the smaller systems there is a central 
body grander far than all the rest, so Lambert believed that 
for all of the larger orders there exists a central orb of corre- 
sponding magnitude. No such central point, no such massy sun, 
about which our sun may be turning, was at hand. Lambert 



388 THE WORLD MACHINE 

therefore imagined one ; and since it would needs be very 
large and on this account conspicuous, if it were aglow like the 
rest, he conceived that these vast central suns were opaque 
and dark. 

It was a pure conceit. There was simply nothing save a 
shadowy analogy upon which the imagination of Lambert had 
to build. His ideas were generally forgotten, or remembered 
only to be flouted. Simon Newcomb, in his Popular Astronomy, 
has this rather tart word : — 

" As not the slightest evidence favouring the existence of 
these opaque centres has ever been found, we are bound to 
say that this sublime idea of Lambert's has no scientific founda- 
tion. Astronomers have handed it over without reservation 
to lecturers and essa57ists." 

In a way this rebuke is still justified. Still, it is curious 
to note how, within a very few years, discoveries have come 
which lend a hint that such opaque centres may exist. These 
might be the dark suns which the spectroscope has revealed. 
Their number, we know already, is great. Whether they be 
companions of glowing suns or not, there seems little reason 
to doubt that eventually the number of dark bodies will be 
found vastly to outnumber those which are ablaze. A sun of the 
probable grandeur of Canopus would have a mass more than 
sufficient to form such a centre of the third order ; and on 
the reasoning indicated, it is much more likely to be dark than 
luminous. 

Perhaps in another half-century or so, we may have some 
basis upon which to estimate the validity of Lambert's con- 
ceptions. At the present time speculative minds may still let 
their fancy rove. The most vital objection which may be 
urged against this view, at least so far as our own solar system 
is concerned, is the apparent absence of any considerable per- 
turbation of the planets. The motion of the moon, we know, 
is very sensibly affected by the sun. If we are revolving about 
some greater sun, it might readily be supposed that it would 
exercise some gravitational pull upon the larger planets in a 
similar way. No equivalent deviation from their orbits can 
be found. It seems fairly certain that there is no body in any 
wise comparable with the mass of the sun within at least a 
thousand times the earth's distance. Between this and 277,000 
times — the estimated distance of the nearest sun — is, of course, 



THE STRUCTURE OF THE UNIVERSE 389 

a long way. Some millions of dark bodies might lie within this 
vast abyss. One of these might be huge enough to be a centre 
of revolution for our system ; we have no present evidence 
of its existence. 

So much for fancy. Scientific method has not been more 
successfuL 

The first to attempt a conception of the structure of the 
universe by induction from observed facts was William Herschel. 
It was, indeed, the great problem of his life. To gain some sort 
of an idea, he set about systematically counting the number of 
stars in different telescopic fields to determine whether there is 
any wide variation in their apparent number. This process 
he called '' star gauging." 

The actual count of the whole heavens was, of course, a 
physical impossibility with such telescopes as he employed. 
These were, for this purpose, not greatly inferior to the best 
which we now have. He therefore counted selected portions 
of the field, and made his estimates accordingly. His industry 
was amazing. Before he was through he had actually made 
computations for 3400 telescopic divisions of the sky. What 
he found was that the stars seemed very much more numerous 
in the direction, or as we may say, the plane, of the Milky Way 
than in the heavens at right angles to this. He therefore con- 
jectured that there might be some definite distribution — in a 
word that the universe, at least such of it as the telescope 
may disclose, does possess a definite shape. 

If it may be supposed that the stars lie at something like 
a general average distance one from the other, the result of 
Herschel's investigations was to confirm in a measure the ideas 
of Wright and Kant. He thought that, looking in the direction 
of the Milky Way, the stellar universe might extend perhaps 
five times as far as in the direction perpendicular to this. 
He did not conceive, however, that this arrangement was per- 
fectly uniform, but that in one direction there is an immense 
bifurcation. The figure which he drew was bizarre enough. 
It resembled a two-legged body with no head. 

Herschel did not himself hold by his two-legged universe. 
Further consideration revealed to him that the assumption of 
equal spacing, or, as we may say, equal star density, might be 
wholly erroneous. His discovery of binary systems and the 



390 THE WORLD MACHINE 

apparent existence of distinct star clusters like the Pleiades 
and others, rendered it highly possible that there are, as it 
were, clumps, of stars. This might be true over vast areas. 

It was evident that a mere count of the stars could not 
settle the question. It was needful to gain some idea of their 
distance. This alone might give some clue as to their relative 
spacing. But in Herschel's time no reliable measures of parallax 
could be made. He therefore conceived a simple method of 
determining relative, if not actual distance. This lay in com- 
parisons of brightness or magnitude. 

If the radiance of the suns be equal, it is obvious that the 
light that comes to us from them will be in proportion to their 
distance, more precisely in inverse proportion to the square of 
the distance. A star twice as far as another will send one- 
fourth the light — it will seem just one-fourth as bright. Then, to 
determine their relative distance, all that remained then was to 
find some method of accurately determining the light of the stars. 

Herschel found this in a fairly satisfactory way in the use 
of telescopes of different powers. In reflecting telescopes 
at least, the amount of light transmitted to the eye of an 
observer is in proportion to the square of the diameter of the 
reflecting mirror. It follows that, on the average, a star four 
times the distance of another will appear of equal brightness 
with the other viewed through a telescope four times as large. 
This, of course, assumes that the stars are of equal size and 
emit light with equal intensity. We know now, of course, 
that the stars vary in size as greatly as the members of the 
solar system — that is to say, in proportions all the way from the 
sun itself down to the minor satellites of a minor planet. We 
know, too, that their light-giving power varies as widely, let 
us say, as from an incandescent electric lamp to an arc light. 
Nevertheless, bunching them by the millions, it is probable 
that the assumption of an equal average size for each " magni- 
tude " is fairly justified, and Herschel's larger telescopes easily 
showed twenty or thirty millions of suns. 

It was on this basis that Herschel estimated that, on the 
average, a star is distant in proportion to its magnitude, and 
that his forty-foot reflector therefore revealed the existence of 
stars 2800 times the distance of Sirius, the brightest of the 
heavens. He assumed, of course, that there is no extinction 
of light across this distance. 



THE STRUCTURE OF THE UNIVERSE 391 

When now he compared the number of stars of average 
equal brightness with the estimates of their relative distance, 
it was found that there was no correspondence. If we were 
to conceive the stars distributed in a series of spheres, or spherical 
shells, one enclosing the other after the manner of a Chinese 
egg, the earth or the sun being supposed at the centre, it would 
follow from the supposition of even spacing that the number 
of stars in each shell would increase in the proportion of the 
cube of the distance. The figures did not correspond. The 
actual number increased much more rapidly in the lesser magni- 
tudes than the theory would suppose. 

Towards the end of his life, therefore, Herschel seems to 
have concluded that it was impossible to set any definite bounds 
to the stellar system ; but he appears more or less to have 
retained the belief that its general shape answered somewhat 
to the conclusions of his earlier research. 

The subject appears to be one of endless fascination to the 
astronomer, and since the time of Herschel a considerable 
number of minds have attempted the problem. One of the 
most notable was the elder Struve, long the director of the 
Pulkowa Observatory. He combined the result of a count of 
the stars of several magnitudes made by Bessel in a wide zone, 
with the gauges of Herschel. He adopted the same theory as 
the latter, supposing that the brightness of the stars supplies, 
on the average, a measure of their relative distance. His con- 
clusions were that the stellar system might be made up of a 
series of layers of varying density, lying parallel to the plane 
of the Milky Way. In the via lactea the stars would be densest ; 
he would conceive that in this layer they are spread out as in 
a wide, thin sheet, with our sun -situated somewhere near the 
middle of the layer. Were we to journey outwards in a direc- 
tion perpendicular to this plane, we should find the stars growing 
thinner and thinner without perhaps ever reaching a boundary. 

Against the hypothesis of Herschel, Struve, and all their 
like, the late Richard A. Proctor, well known as a writer on 
the more popular side of astronomy, brought forward objec- 
tions that seem decisive, at least so far as our present know- 
ledge extends. One was as to the assumption that the stars 
are more or less alike in their actual light-giving power. Stars 
that we now know to be of very nearly equal distance may vary 



392 THE WORLD MACHINE 

in their apparent brightness by hundreds and perhaps thou- 
sands of times. Such is the case, for example, of Sirius and 
6i Cygni. This difference may be due to a vast disparity in 
size ; it may be due to an equally wide disparity in their tem- 
perature or light-giving power. The apparent brightness, there- 
fore, is only the vaguest sort of a clue to the distance. It is 
actual measures of parallax alone which could ever afford a 
sure basis for safe induction. 

Proctor likewise brought forward the argument from the 
apparent drift of the stars. Here and there over the heavens 
the stars of certain regions, at least such as disclose an apparent 
motion, seem moving in a common way. Their motions may 
not be at all equal, but have the same general direction. It 
is just as if throughout the spaces of the sky there were cur- 
rents and eddies as in a stream of water. This Proctor aptly 
described as " star drift." It may be entirely an illusion, a 
happen-chance, depending on our point of view ; but if it have 
any underl5dng reality, it is evident that this would result in 
agglomerations of stars in one region with relative emptiness 
in another. If such systems exist, it is clearly hopeless to 
suppose that our present means are sufficient to attain any 
definite ideas as to universal structure. 

Carrying out his conception of star drift, Proctor was led 
to conceive the Milky Way as an irregular spiral stream of 
minute stars lying in and among the larger stars of the system. 
That all this could be little more than guess-work is evident 
from the conclusions of Madler. Drawing naturally upon much 
the same material, Madler conceived the stars of the Milky 
Way as entirely separated from the rest of the stellar system 
and as belonging to an outlying ring or system of rings. In 
order to account for the gaps in the Milky Way, this ring was 
supposed to be cleft on one side. It is on this account often 
referred to as the ** cloven ring " theory. In this view the 
stellar system, viewed from without, might present some such 
an appearance as a split key-ring, spread out a bit. The outer 
ring, cleft on one of its sides, would represent the system of the 
Milky Way, while the luminous mass in the centre would include 
the remainder of our stellar universe. Madler likewise enter- 
tained the idea of a central sun. 

It cannot be said that we are any further advanced at the 



THE STRUCTURE OF THE UNIVERSE 393 

present day. It is evident that the data which we have to go 
on is as yet insufficient. In a recent volume,^ and in a 
later monograph, Simon Newcomb, himself the foremost living 
student of this especial subject, sums up the slender conclusions 
which seem warranted thus far. He believes that the collec- 
tion of the stars which we call the universe is limited in extent. 
The smallest stars that we see with the most powerful tele- 
scopes are not necessarily more distant than those of a grade 
brighter, but are rather smaller or less luminous stars. This 
does not preclude the possibility that far outside of our universe 
there may be other collections of stars of which we know 
nothing. 

The boundary of this especial universe is apparently some- 
what indefinite and irregular. As we go outwards towards the 
boundaries, the stars may thin out gradually. It does not seem 
possible to decide whether the agglomerations of the Milky 
Way lie on this boundary or not. 

Seeliger of Munich would go a little further. This astronomer 
made an exhaustive study of the distribution of the great mass 
of stars relative to the so-called Galactic Plane. But the inquiry 
extended only to stars of the ninth magnitude — that is to say, 
to a few hundred thousand out of, possibly, hundreds of millions. 
Within these limits there does seem an unmistakable increase 
of star density in the region of the Milky Way, and a progressive 
decrease in either direction perpendicular to this plane. In 
other words, these hundreds of thousands of brighter suns 
seem collected into some such a mass as that imagined by 
Herschel and Struve. In Seeliger's view, " the Milky Way is 
no merely local phenomenon (local to us), but is closely con- 
nected with the entire constitution of our stellar system." 

This idea is somewhat strengthened by the researches of 
Celoria, the successor of Schiaparelli, at Milan. Celoria utilised 
a very much larger number of stars ; his results were much 
the same. But one circumstance is to be noted. From the 
star gauges made by the Herschels, father and son, the crowd- 
ing of the stars in the Galactic Plane appeared to be perhaps 
twenty times more intense than towards the Galactic Poles — 
that is to say, in the regions at right angles to this plane. 

From the later studies of Celoria and others, it does not 
appear that this Galactic star density is more than two or three 

^ Newcomb, The Stars, 1902. 



394 THE WORLD MACHINE 

times that of the poles. The studies of Pickering of Harvard 
would reduce this to certainly not more than two times. The 
discrepancy is due simply to the fact that the later counts go 
further, the averages involve enormously greater numbers. The 
inference is that if the investigation were carried very much 
further — if it were possible, to stars of the fifteenth magnitude 
or beyond — this difference of star crowding would quite dis- 
appear. 

It win be seen, therefore, that as yet the problem is un- 
solvable. It may be that the appearance of a grindstone steUar 
aggregation is simply an illusion. It may, of course, always 
be that it has no boundary, or, possessing a boundary, this 
may lie for ever beyond our means of discovery. Before we 
can form any idea of shape or of finitude, there is a fundamental 
question which must be solved. This is the extinction or ab- 
sorption of light. 

Our present theory of light was suggested and is to some 
extent based upon the analogy of sound. We know that sound 
is a wave process. In conceiving of light as of a similar nature, 
the most, though not all, of the observed facts may be quite 
satisfactorily accounted for. We know that the vibrations of 
sound are progressively damped down by the medium in which 
they are propagated — in other words, that they eventually 
wear out against the friction of the medium. The conception 
of a light-carr37ing medium involves the idea that the ether is 
to aU intents frictionless. This is, of course, a philosophic 
absurdity, if we conceive the ether to be of a material nature. 
The inference, therefore, is that sooner or later the vibrations of 
light would be extinguished by the medium through which they 
travel. It may be, of course, that the whole ether theory will 
later be discarded, and that there is no necessity for this con- 
clusion. 

Be that as it may, we now know that space is nothing Hke 
so empty as was formerly supposed. It is booming with suns 
and probably a vastly greater number of dark bodies. If our 
planetary system, with five or six hundred permanent members, 
is an image or type of solar arrangements in general, the number 
of planets, satellites, asteroids, and comets may be hundreds 
or thousands of times the total number of central masses, 
glowing or dark, just as the number of dark suns may be 
hundreds or thousands of times those of the visible suns. 



THE STRUCTURE OF THE UNIVERSE 395 

This is a first fact. The swarms of meteors is a second. 
Space is teeming with them ; they may be the fundamentals 
of the universe. Their number is vast beyond all computation. 
Seen through a section hundreds of thousands of millions of 
miles thick, they could hardly be perfectly translucid. 

And besides all this there is cosmic dust. It is microscopic 
in dimensions, possibly less than a thousandth of a millimetre 
in average diameter. However, the stars are very far. Arrhenius 
has computed that no more than one hundred such minute 
particles, distributed evenly through every cubic kilometre of 
space, would, at the distance of the farther stars, suffice to 
block their light from our view. 

In view of all this, it becomes highly improbable that the 
light of all the stars reaches our eyes undimmed. It is possible 
that this accounts for the fact that the heavens are not eternally 
ablaze, and why a billion of blazing suns in no wise affects the 
temperature of the earth. It may be that we see the stars 
as through a veil, and that the more distant of them are nothing 
like so far away as our present estimates suppose. This, of 
course, in no wise touches the distance of those whose parallax 
has actually been determined ; but these are hundreds against 
many millions. It may well be that the stars of the eighteenth 
magnitude are nothing like a thousand times as far away as 
the average of the first magnitude stars, as the present theory 
supposes. 

The question will probably find decisive answer from in- 
vestigations that are now being carried out. Professor Comstock 
of Washburn Observatory has recently brought forward the 
evidence to show that either the more distant stars have in- 
dividually less light-giving power, are actually smaller or fainter, 
or else that at great distances their light does suffer some diminu- 
tion, some absorption. There seems, of course, no reason to 
suppose that the actual size or luminosity of the stars is any 
less in one particular region than in another. The conclusion, 
therefore, is for absorption, and Professor Comstock endeavours 
to find what factor of absorption, mathematically expressed, 
would account for the facts he has brought out. 

If such an absorption takes place, it is obvious that we 
shall never know much about the farther reaches of the stellar 
system, and nothing at all of its possible boundaries or shape. 
We shall, to be sure, steadily advance in our knowledge of 



396 THE WORLD MACHINE 

regions less remote. It may be that with this steady advance 
the nearer of the stars will be found aggregated into systems 
as orderly and as simple as that of our planetary arrangement. 
It may be that from this we shall attain to some more or less 
definite conceptions of the rest. They would never be more 
than the fancies of Lambert — inferences from analogy. 

Of more proximate interest is the question as to whether 
our own sun is a member of any immediate system of stars. 
Already there is a shght suggestion that it may be. A very 
ambitious attempt at an orderly arrangement of the nearer 
stars was made some years ago by Maxwell Hall. 

His reasoning was simple. If the sun is revolving about 
any central point, it is obvious that this point will be more or 
less at right angles to the line of its present motion. From the 
known proper motions of the nearer stars, Hall endeavoured 
to fix such a point and to bring these known motions into agree- 
ment with this idea. His results did not tally with the obser- 
vations. His work remains, therefore, merely a magnificent 
attempt. It may be that in later days it will be possible to take 
up the problem with more hopes of success. It is, however, 
based upon the idea that the force of gravitation is sufficient 
to hold the suns to such an orbit. At the present time, as we 
shall see, this is doubtful. 

It follows, therefore, that the conceptions we may make of 
stellar arrangement are yet of the vaguest. It may be that 
no such arrangement in the sense of definite systems exists. 
We might here have recourse to the analogy of molecular and 
molar motions, such as they are known to us. 

If there were aught in Lambert's vast ideas of systems 
within systems, we might readily suppose that the succession 
of " orders " which he imagined might extend inwards towards 
the infinitely little as well as outwards towards the infinitely 
vast. We might discover a like order in the structure of matter. 
We might find, for example, that the atoms and molecules of 
the chemist likewise possess a planetary arrangement. It is 
curious to note that this is precisely the drift of present-day 
conceptions of atomic structure. 

In the light of recent research, especially of Professor 
J. J. Thomson of Cambridge University and his school, we 
may conceive the atom as made up of a relatively large number 



THE STRUCTURE OF THE UNIVERSE 397 

of ultimate units — ultimate so far as our present knowledge 
extends — and there seems reason to suppose that these ultimate 
units comprise more or less of a planetary system. It seems 
even as if we should be able to compute the times of revolution 
of these ultra- atomic satellites, though it is not yet clear as to 
whether there exists a central and attracting mass. 

The atoms themselves may constitute minute systems ; they 
may in their turn be arranged into what we might term mole- 
cular systems. A noteworthy attempt in this direction was 
made some years ago by the distinguished Russian chemist, 
Mendeleeff. He endeavoured to represent the arrangement of 
the atoms within the molecule as following a Newtonian order, 
and perhaps ruled by Newtonian law. Neither of these concep- 
tions represents as yet anything more than ingenious conjecture. 
But even if they should be confirmed, it is noteworthy that in 
the next step higher we may be certain that any planetary scheme 
of arrangement distinctly ceases. 

The motions of the molecules in a free or vaporous state are 
known with a high degree of probability. For definite tempera- 
tures the motions of the molecules of the air and of other gases 
may be computed with considerable accuracy, at least as to 
their average speeds. This constitutes our modern, or, as it is 
termed *' kinetic," theory of gases. It regards the pressure 
which a gas exerts upon the walls of a bounding vessel as de- 
termined by the number and force of the molecular particles 
bombarding the walls of the vessel. But within the gas itself 
no order or systematic arrangement obtains. The molecules 
are conceived as flying about in every direction at a tremen- 
dous rate of speed, coming into collision one with another, and 
rebounding without loss of energy. 

So far as our present knowledge goes, the myriads of the 
stars present, in their motions, rather the image of the mole- 
cules of a gas than any arrangement of suns and planets and 
satellites such as was pictured in the dreams of Lambert. To 
the eye of the universal mind, the suns may be as the ultra- 
microscopic particles of the air sporting hither and thither in 
confused and incessant flight. The dance of the motes in a sun- 
beam penetrating the shutters of a dark room may be, for aught 
we know, the mirror of cosmos. Perhaps the picture will be 
more vivid if we were to recur to the simile already employed, 
that of a school of dancing fireflies, flashing out their light 



398 THE WORLD MACHINE 

through a moment of cosmic time, then to go dark until through 
a process of fertihsation and rebirth they bhnk and gleam 
again in unending cycles. The suggestion is but a fancy. The 
problem is transcendent. We do not know ; it is possible 
that we never shall. 

Probably it is among the naivetes of our intellectual child- 
hood to suppose that the pursuit of the scientific method will 
ever bring us any nearer to the ultimate mystery of creation 
than were the favoured children of Hebraic tradition. Doubtless, 
no more complete illusion ever possessed the human mind than 
that through its operations we may penetrate the origin of 
things. So far from reading any Reason or Intelligence into 
this strange wentle-trap of a world, the amazing insight into its 
more concrete processes, its mechanical device, which the last 
few centuries have brought, leads to utter bewilderment; it 
seems to the initiate eye yet stranger, yet more mystic, more 
unthinkable, more unbelievable, than ever. 

The conception of a creative Being was simple — perhaps, in 
the mists of primitive ignorance, imaginable. This is true no 
longer. Our modern knowledge has pushed back immeasurably 
the Hmits of the world ; it has disclosed the immeasurable 
duration of time. It has given us a rational account of the 
planet on which we live, the system of which we form a part. 
It has indicated a probable origin and a probable end. In some 
relative sense we know where we are; in some relative sense 
we know how we came to be here ; in some sense we know less 
than ever why. What is still more, we know now that we do 
not know, and that in all finite probability we never can. 

The cosmic structure may be for ever beyond our human 
ken, alike with cosmic ends and cosmic aims. There may be 
limits beyond which we cannot pass. But the area within 
these limits is vast — field enough for a splendid human work. 
We have learned to know the processes of human birth, the 
course of human evolution. We have learned to know in its 
larger outhnes of the evolution of worlds. If the grandeur 
of our thoughts be measured by the immensities of space and 
time which they cover, surely no human thought has ever 
reached nearer to the essence of sublimity than this. We have 
cast aside the heavy trammels of our daily cares and daily needs 
to search for cosmic order ; let us turn to view the ways of 
cosmic time. 



CHAPTER XXXI 
THE BIRTH AND DEATH OF WORLDS 



Of old hast thou laid the foundation of the earth : and the heavens 
are the work of thy hands. 

They shall perish, but thou shalt endure : yea, all of them shall 
wax old like a garment ; as a vesture shalt thou change them, and 
they shall be changed. 

Psalm cii. 25, 26. 



MUTABILITY 

From low to high doth dissolution climb, 

And sink from high to low, along a scale 

Of awful notes, whose concord shall not fail : 

A musical but melancholy chime, 

"Which they can hear who meddle not with crime. 

Nor avarice, nor over-anxious care. 

Truth fails not ; but her outward forms that bear 

The longest date do melt like frosty rime, 

That in the morning whitened hill and plain 

And is no more ; drop like the tower sublime 

Of yesterday, which royally did wear 

His crown of weeds, but could not even sustain 

Some casual shout that broke the silent air. 

Or the unimaginable touch of Time. 

Wordsworth. 



CHAPTER XXXI 

THE BIRTH AND DEATH OF WORLDS 

In the sixty or eighty years intervening between the discovery of 
the telescope and the publication of Newton's Principia, man- 
kind penetrated more deeply into the mystery of his surroundings 
than in all the previous years of his intellectual life. These 
sixty or eighty years saw the establishment of the Coppernican 
system, of the science of mechanics, of the law of gravitation, 
of the true dimensions of the solar system ; with it the little- 
ness of the earth, the grandeur of the sun, the almost infinite 
distance of the stars. It was within this period that man 
learned to know at last his true place in creation. 

When this vast work was complete it would seem as if 
natural investigation could no further go. But the inherent 
impulse of the mind forbids a stop. Coppernicus had shown 
the true system of planetary orbits, Kepler had established 
the laws of planetary motion, Newton had revealed the cause 
and binding force. There still remained the profound question 
which had agitated the mind of man from the earliest time 
in which he had begun to reflect upon existence. This was 
the origin of the world. In so far as they were not simply 
systems of conduct and morality, or mere rescripts of the his- 
tory of an especial people, what we call religions represent 
mainly an endeavour to solve this profound problem. Practically 
all of the various faiths of the various peoples included some 
essay in cosmogony. 

These early endeavours were naturally crude. Few of them 
had any material basis either in fact or in observation. They 
were for the most part merely like the extraordinary stories 
which spring up in the minds of highly imaginative children ; 
they represent in truth simply the intellectual childhood of the 
race. Brahma in meditation on the lotus leaf through long 
ages, producing at length a golden egg as large as the universe, 
out of which the latter was slowly evolved, is a type. The 

401 2 c 



402 THE WORLD MACHINE 

Chaldean tradition of a Garden of Eden, the Deluge and the 
rest, the basis of the Mosaic system, is another. It was the latter 
which survived among the peoples of Europe when Hellenic science 
had gone down, and until the later years of the seventeenth 
century. After the generation of Cassini and Newton it could 
no longer satisfy any rational mind. 

The telescope had cast the world adrift ; cosmos seemed to 
have no whence and no whither. It produced a sort of an 
intellectual simoon. When the tumult had somewhat subsided, 
when it finally became clear that the facts were impassable 
rocks, speculative minds began to cast for an anchorage. If 
the Chaldean tradition was no longer tenable, still was there 
never a creation at all ? Did the universe, and especially that 
little part which is ours, for ever exist as it is ? 

We know that the speculative brain of Newton sought 
vainly in the phenomena which he had investigated so deeply, 
for some sort of a clue. Too heavily weighted by prevailing 
dogma, too deeply occupied perhaps during the period in which 
his mind was really active — that is to say, before his mental 
illness — with the immediate mechanical theory of planetary 
movement, he could discover no opening. The problem passed 
to a newer generation, upon whom tradition had less weight. 

Almost contemporaneously with the Principia, Fontenelle 
had rescued from oblivion the glowing fancies of Bruno, and 
speculated delightfully upon the plurality of systems and worlds. 
Huyghens' reveries upon the same subject, published posthu- 
mously, came ten or twelve years later. Leibnitz about the 
same time had conjectured that the planets are extinct suns ; 
he had seen that the flattened shape of the earth indicated 
beyond peradventure that it had once been in a fluid condition. 
He divined that it had once been a molten mass. In 1734 
Daniel Bemouilli had undertaken some remarkable calculations, 
demonstrating on the calculus of probabilities that the solar 
system could not have been the product of chance. This was 
the state of speculation when the subject was taken up by 
Buffon. 

It is to this great naturalist that we owe the first attempt 
upon thoroughly scientific principles to conceive the origin of 
the globe on which we dwell. His ideas were contained in a 
volume on the Theory of the Earth, first published it 1745. 
Four years after it was incorporated as the first volume of his 



THE BIRTH AND DEATH OF WORLDS 403 

celebrated Natural History, cherished companion of the mind 
of youth. Let us take note of the facts upon which he had 
to build. 

The earliest observers, to whom the truth had become clear 
that the planets travel in circles, must have likewise noted that 
they all travel the same way. Some among them may have 
noted that the circling path of the moon is in the same direc- 
tion. When the heliocentric ideas of Aristarchus had been 
established, it was found that the earth was journeying the 
way of the rest. All this could hardly be mere coincidence. 

Then came the discovery of the various satellites — first of 
Jupiter, then of Saturn. All of these revolve about their 
central orbs in the same manner as the moon. Finally, it was 
observed that the earth's revolution upon its own axis was in 
the same direction. So it was found were the revolutions of 
all the other planets, and finally that of the sun, as one by one 
they were revealed by the telescope. 

Putting all these motions together, Bernouilli had calculated 
that, in the theory of chance, it was millions to one that this 
could not be due to mere hazard. Whatever force, whatever 
power, had impressed this especial direction of motion upon 
one had evidently acted in the same way upon all. 

Moreover, there was another curious fact. If one could 
take up a point of observation somewhat distant from the 
outermost rim of the solar system, he would observe that the 
whole of the planetary motions take place within a thin plane. 
If we project through the intervening spaces the disk which 
the ancients had named the ecliptic, or plane of eclipses, it is 
noted that none of the planetary orbits are inclined very much 
above or below this median line. Altogether, the steepest 
of the inclinations, at least in Buffon's time, did not exceed 
one-seventeenth part of the sphere of the heavens. This could 
be as little the outcome of chance as the common direction of 
movement. What was the determining cause of this striking 
uniformity ? 

The mind of Buffon found a hint in the calculations of 
Newton as to the relative mass of the planets and the sun. 
Newton had computed that the mass of the known planets 
and satellites put together would not equal the 650th part of 
the mass of the sun ; we know now, of course, that even with 



404 THE WORLD MACHINE 

500 satellites and two new planets added, it is still less than 
a 750th. The quantity is very small. If a 750th part were 
chipped off a cannon-ball or a melon, neither would greatly 
suffer. The trained imagination of the investigator of nature 
swept swiftly to the thought — perhaps here is the explanation. 

Buffon put with this Newtonian computation another of 
his own. Knowing the distance of the planets and their ap- 
parent diameters, it is a simple enough matter to calculate 
their volume ; that of the sun as well. The volume divided 
by the mass is the measure of density — that is to say, the unit 
quantity of matter in a chosen unit of space. According to 
Buffon's calculation the average density of the planets is to 
that of the sun as 640 to 650 ; in a word, the relation was 
very near to unity. But if the stuff of the planets is of the 
same density as that of the sun, then it is next to certain that 
it is the same stuff. The figures were in error ; but the con- 
clusion was true. Remember that this was more than 150 years 
ago, a long time before the development of chemistry, a century 
almost before the use of the spectroscope ; it was an intuition 
of genius. 

With this discovery there seemed little question, then, that 
our little earth and all its kind were once a part of the sun. 
Somewise or other these planetary bits had been thrown off, 
brushed off, from the glowing mass, had cooled down into 
solid orbs and taken up their common way around the parent 
sun. It was a splendid guess — but how had it come ? 

There were dozens of ways, of course. There might be vast 
eruptions upon the sun like those upon the earth which had 
destroyed Pompeii. There might be colossal explosions hke 
that which in our own time blew away the island of Krakatoa. 
Buffon thought of another. Up to this time he had been 
following the firm path of induction, now he struck off into 
analogy and guesswork. The study of comets, the plotting 
of their orbits, the prediction of their return, was the order 
of the day. Some of them were very vast — they moved at 
frightful speed. Newton had shown that some of them smash 
into the sun, some just graze its edge. It was known that some 
of them at least come probably from beyond the confines of our 
planetary system. Was it not conceivable that from some- 
where in the distant ways there had come one of especial power 
and great bulk, rushing along with such impetus as to cut 



THE BIRTH AND DEATH OF WORLDS 405 

straight through the Hmb of the sun and carry away a bit of its 
flesh ? It was a tempting hypothesis, not in the least un- 
scientific, easily possible in the existing state of knowledge. 

Buffon argues for his theory with tenacity and conviction, 
and with all that grace of style which made him one of the 
most widely known of writers upon natural science. But after 
all it was only a guess ; it had no facts to go on. Nothing in 
the way of subsequent discovery ever came to its support. But 
it laid a sohd foundation whereon others might rear a more 
enduring fabric. The central fact which Buffon had laid bare, 
not indeed with firm proof but with a high degree of probabihty, 
was that the matter of our solar world at least is of the same 
piece. It was a hundred years before it could be proved ; but 
his surmise set men thinking, and led others to happier results. 

A few years before Buffon, the mathematician Maupertuis 
had drawn attention to the curious shape of some of the vague 
nebulous masses which no telescope of the period could resolve 
into separate stars. Some of them appeared to have a figure 
like that of an oval or ellipse. If Buffon had not been so hot 
upon the trail of his sun-scraping comet, he might have seen 
that here was a hint of value. He let it go by. In the far 
away little university town of Konigsberg, on the upper edge 
of Germany, there was a young philosopher with a teeming 
brain to read after him with better eyes. 

The early years of the century had seen a lively polemic 
among the mathematicians over what the French call forces 
vives — that is, the energy contained in a body in motion. It 
really bore on the ground principles of a rational dynamics. 
Galileo had laid the foundations ; Huyghens, Leibnitz, and 
Bernouilli had made important contributions ; the matter was 
finally planted on a firm basis, not subsequently to be dis- 
turbed, by Euler in 1736 and d'Alembert in 1743. 

But the old Cartesian ideas were still floating about, ghosts 
from a once splendid fabrication which the Newtonian philo- 
sophy had woefully undone. A few years after d'Alembert, 
a young man fresh from his university studies dashed into the 
arena with an effort to bring back life to the ghosts. One does 
not readily recognise under this guise the familiar figure of the 
metaphysician, Immanuel Kant. He was born in Konigsberg, 
the son of a saddler ; as his name indicates, of Scottish descent. 



4o6 THE WORLD MACHINE 

He had studied theology and the sciences in the university of 
his native place, become first a private tutor, then a privat 
docent in the university. Years afterwards he was given a 
professorship. This he held to the end of his lengthened days, 
never venturing, so the story runs, beyond ten miles outside 
the place of his birth. 

He had a devouring mind ; his mathematical studies had 
given him a lively interest in scientific problems. Five or six 
years after the appearance of Buffon's Theory of the Earth 
he came across a copy of the Hamburg Free Opinion, which 
contained a summary of the contents of Thomas Wright's re- 
markable volume, wherein the grindstone theory had been 
announced. Wright was not content to figure out the shape 
of the stellar universe, but indulged in some interesting specula- 
tions as to its history as well. It was stimulating. Kant 
was then twenty -seven, the age at which Darwin reached his 
conception of natural selection. Four years after he appeared 
with the vigorous essay in which the nebular hypothesis was 
for the first time laid down. 

The slender volume bore the title of " General Natural 
History and Theory of the Heavens ; or, a Research in the 
Construction and Mathematical Origin of the Entire Universe 
on Newtonian Principles." It contained a fulsome dedication 
to the " Very Enlightened and Very Mighty King and Sire," 
Frederick II. of Prussia. Neither the sounding title nor spread- 
ing dedication saved it from a dismal fate. The publisher of 
it straight away went into bankruptcy. It never really saw 
the light of publicity until long years thereafter. Moreover, 
it was published anonymously, and in the years that followed 
this promising student of the attainable had gone wandering 
in the desolate bogs of philosophic speculation, the undoing of so 
many briUiant minds. In a characteristic essay on The Only 
Possible Argument for the Existence of God, published in 1763, 
he gave a summary of his theory. But it did not really come 
before the public until 179 1, then only as an appendix to 
a German edition of Herschel's Structure of the Heavens. 
Though the fame of Kant by that time was great, it seems 
to have attracted little notice even then. 

It was in many ways an amazing book. Its central idea 
is a paraphrase from Descartes, of more than a century before : 
" Give me matter and I will build a world " But he will build. 



THE BIRTH AND DEATH OF WORLDS 407 

not out of the cobwebs of his mind as did Descartes, but from 
the newest and soUdest knowledge of the day. You will often 
read that this effort of Kant's was a mere speculation. Such a 
remark could come only from ignorance of the work itself. Kant 
had deeply studied Newton ; he had studied Buffon ; he was 
abreast with the scientific progress of his time. He sought a 
mechanical explanation of cosmos, and he found it in the law 
of gravitation. With the aid of this he endeavoured to group 
the known facts of cosmogony into a working theory. How 
well did he succeed ? 

Wright of Durham had pictured the Milky Way as an especial 
system of stars. With this thought Kant links the observation 
of Maupertuis as to the nebular patches in the sky. The latter 
can be, he says, nothing else than similar heaps of stars. Since 
they appear to have an ellipsoid form, they probably possess 
the same shape as the galactic system to which we belong. 
More or less after the fashion of Lambert, Kant saw the universe 
as made up of endless systems, of which our own is but a part, 
and of which in turn our solar system is more or less a model. 
The universe is for him infinite and endless ; we rise from 
system to system until the mind is lost in a confused effort 
to comprehend infinitude. 

He considers that gravitation is universal, estimates that 
if any of the fixed stars belong to our system they may be so 
distant that it would require a century of observation to disclose 
their apparent motion. But if the universe be made up of 
similar systems, it is evident that we have but to study the 
one nearest at hand to understand the formation of them all. 
If now we examine our especial planetary arrangement, we find 
six considerable bodies — the number then known — revolving in 
a common direction ; between them space is empty. There 
seems only one way that this common motion could have been 
impressed upon these widely separated bodies : they must once 
have been all of one piece. In a word, these empty spaces 
were once filled with a diffused material which, under the in- 
fluence of gravitational attraction, would have steadily drawn 
together. He says :— 

** I assume that all the material now contained in the various 
globes which belong to our solar world, in the beginning of 
things was resolved into an elementary ground-substance occu- 
pying the entire extent of the world in which the planets and 



4o8 THE WORLD MACHINE 

comets now circulate. This condition of nature, regarded 
simply by itself, appears to be the simplest which can follow 
upon nothing. But this condition of general quiescence could 
last but a moment. The elements have within themselves the 
essential forces needful to set them in motion, and have in 
themselves a source of life. This matter at once reveals an 
effort to take on form. The scattered elements of like density 
come together by virtue of the force of attraction to form a 
sphere, around which will gather the substances of less specific 
gravity." 

It is in such wise that he conceives the beginnings of the 
world, and this hypothesis he endeavours to firm ground through 
a hundred and fifty closely reasoned pages. He brings to bear 
the density and comparative mass of the different planets, 
their spacing one from another, the eccentricity of their orbits, 
endeavouring everywhere to find sequence and law. Having 
shown that the theory will, as he beheves, satisfy existing con- 
ditions, he turns to the recently discovered rings of Saturn as 
proof that the mode of planetary formation which he has con- 
ceived is the actual mode through which all of the planets have 
passed, and of which Saturn, the outermost, represents the 
last stage. 

It is in his endeavours to show that the contraction of a 
vast nebular mass would result in the formation of a series of 
planets such as our system presents, that Kant's reasoning is 
the least satisfactory. He supposes that the coalescing mass 
would acquire a rotatory motion, and that this motion would 
survive in the successive clumps into which the mass would 
condense. It is not at all clear that this would be the case. 
Moreover, on Kant's own theory the apparent result of the 
contraction of a vast mass would not be a planetary system at 
all, but that it would aU draw towards a common centre — 
that is to say, the sun. 

The available facts which Kant had to build on were in- 
adequate, and some of the inferences which he drew have 
been discredited by subsequent discovery. The young Konigs- 
berg philosopher failed in his ambitious attempt to provide 
a satisfactory mechanical explanation of the origin of worlds ; 
he did not become a greater Newton. It may be remarked 
that no one has succeeded since. The precise process eludes 
us still. That our solar system and all its kind grew out of 



THE BIRTH AND DEATH OF WORLDS 409 

more or less nebulous masses there are few now to doubt, though 
we may not yet know how. The recognition of this probable 
origin we owe to Immanuel Kant. 

It is not without interest nor without significance that 
while Kant's ill-fated little work was lying upon the musty 
shelves of the booksellers, unnoticed and unread, the splendid 
mind of Herschel should have been travelling towards much 
the same conception by an entirely different route. Herschel 
had a boundless curiosity to know of everything which the 
heavens contained ; the nebulous patches of the sky, as we 
have seen, interested him deeply. When he began, the number 
known was not large. His first catalogue offered to the Royal 
Society a thousand. He made two more. These wisps of light 
fascinated him as they baffled him ; he hardly left off thinking 
about them to the end of his life. 

The most interesting discovery that Herschel made about 
them was a seeming gradation in what might be termed the 
degree of nebulosity. Some of them seemed clearly nothing 
but cloud, some seemed mottled as though they contained 
denser masses. These denser masses graduated into clusters 
of stars. From the milky nebulosity seen in Orion, up to a 
coarse cluster like that of the Pleiades, there was no line of 
demarcation. At first Herschel was inclined to think that with 
a sufficiently powerful telescope all the nebulae might be re- 
solved into star-heaps. Conceiving that each of these assem- 
blages might be in grandeur and structure something like unto 
our own Milky Way, he made a little jest one day to the effect 
that he had discovered fifteen hundred new universes. 

Later on his views changed. He came to see that there 
were apparently nebulous stars, twinkhng points surrounded by 
a sort of halo. He came to the conclusion that the nebulosity 
about the star is not of a starry nature. It was in thus wise 
that he came to the view that some of the nebulae at least 
might be " a shining fluid " of a nature wholly unknown to us. 

From this came a vast conception, engaging in its simplicity, 
immense in its embrace. It was that the gradations he had 
noted in the appearance of these clusters in reality represented 
epochs of development, stages of world growth. He conceived 
that some " clustering power " might be at work converting 
these diffused and milky masses into brighter and more con- 



4IO THE WORLD MACHINE 

densed objects which would one day result in suns and systems. 
There was a vein of the poet in his nature ; he must, too, have 
been a lover of flowers, for this is the analogy which comes 
to his mind. To such as imagine that scientific papers are 
always arid productions, unrelieved by the touch of fancy, 
a paragraph from his paper may be of interest : — 

" This method of viewing the heavens seems to throw them 
into a new kind of light. They are now seen to resemble a 
luxuriant garden, which contains the greatest variety of produc- 
tions, in different flourishing beds ; and one advantage we may 
at least reap from it is, that we can, as it were, extend the 
range of our experience to an immense duration. For, to con- 
tinue the simile I have borrowed from the vegetable kingdom, 
is it not almost the same thing, whether we live successively 
to witness the germination, blooming, foliage, fecundity, fading, 
withering, and corruption of a plant, or whether a vast number 
of specimens, selected from every stage through which the 
plant passes in the course of its existence, be brought at once 
to our view ? " 

Herschel had reached this view in the years from 1789 to 
1791. It was in the latter year that Kant's tract upon the 
nebular theory was reprinted as a tailpiece to a German 
edition of Herschel's Structure of the Heavens. The one was 
at the time the most celebrated observing astronomer, the 
other the most widely read philosopher, in Europe. The 
book could hardly have failed to attract widespread attention, 
particularly from the astronomers themselves. 

It was five years after this that Laplace produced his popu- 
lar Exposition du Systeme du Monde. At the close of this 
work Laplace devotes three or four pages to a criticism of 
Buffon's cometary-impact theory of planetary origins, then 
adds a brief three paragraphs sketching a theory which he 
presents as his own. That Laplace had read Herschel is evident 
from his own pages ; whether he had read Kant is not so clear. 
He mentions neither the one nor the other. It may be noted 
that in this same section of his work he had borrowed from 
Bailly's Histoire an extended argument as to the probable 
agreement of ancient measures of the earth ; he gave it with 
an air of novelty, but without a line or a word of credit. 

The theory of Laplace differed in some essential ways from 



THE BIRTH AND DEATH OF WORLDS 411 

that of Kant ; in the main it was broadly the same. In the 
third edition of the Exposition, pubHshed twelve years later, 
he made some slight additions, and it is on the basis of these 
rather than his first sketch that it has become customary to 
speak of him as the author of the Nebular Hypothesis. Its 
originator he certainly was not. By that time (1808) the idea 
of nebular origins was common property. 

What there was in Laplace's exposition of the theory 
original to him is so brief that it may be stated in his own 
words. He reviews the calculations of Daniel Bernouilli, with- 
out, however, any reference to the latter or to his papers. 
The number of planetary motions had been somewhat increased 
by the discovery of Uranus and numerous satellites ; he con- 
cludes that the chances then are 137,000 milHons to one that 
the system did not arise in any fortuitous way. He dismisses 
the conjectures of BufTon as unable to explain four out of five 
of the principal planetary phenomena, then proceeds : — 

" This hypothesis, being very far from satisfying the re- 
quired conditions, let us see if it is possible to rise to their true 
cause. Whatever be its nature, since it has produced or im- 
pressed the movements of the planets and the satellites, it 
must have once embraced all of these bodies ; and considering 
the prodigious distance which separates them, it can only have 
been a fluid of immense extent. In order to have given them 
a movement almost circular around the sun, and in the same 
direction, it is necessary that this fluid must have once sur- 
rounded the sun like an atmosphere. Consideration of the 
planetary movements leads us to believe that, by virtue of 
an excessive heat, the atmosphere of the sun once extended 
beyond the orbits of all the planets, and that it has successively 
contracted up to its present limits ; this might have taken 
place by reason of causes similar to those which occasioned 
the brilliant luminescence through several months of the famous 
star that was seen of a sudden in 1572, in the constellation of 
Cassiopeia. 

" The great excentricity of the orbits of the comets leads 
to the same result. It indicates evidently the disappearance 
of a large number of orbits less excentric. This in turn supposes 
an atmosphere around the sun which extended beyond the 
perihelion of observable comets, and which in destroying the 



412 THE WORLD MACHINE 

movements of those which have traversed it during the period 
of its vast extent, ended by uniting them with the sun. It 
will be seen, then, that only such comets now exist as lay out- 
side of this area during this interval. As we can only observe 
those which approach rather near to the sun in their perihelion, 
their orbits must be very excentric. But at the same time it 
is seen that their inclination must offer like irregularities as 
if these bodies had been projected at hazard, since the solar 
atmosphere in no wise influenced their movements. Thus, the 
long period of the revolutions of the comets, the great excentricity 
of their orbits and the variety of their incHnations, is explained 
very naturally by means of this atmosphere. 

" But how has the latter determined the movements of 
revolution and of rotation of the planets themselves ? If these 
bodies had penetrated into this fluid mass (from the exterior), 
its resistance would have caused them to fall into the sun. One 
may surmise, therefore, that they have been formed out of 
successive limits of this atmosphere, by the condensation of 
zones which it has abandoned in the plane of its equator, in 
the cooling and condensing of the surface of this star, as we have 
seen in the preceding pages. One may conjecture further that 
the satellites have been formed in a similar manner from the 
atmosphere of the planets. The five phenomena already alluded 
to (similarity of movement, slight excentricity, &c.) follows 
naturally from this hypothesis, to which the rings of Saturn give 
an added degree of probabihty. Finally, if in the zones succes- 
sively abandoned by the solar atmosphere there were molecules 
too volatile to unite among themselves^ or to the celestial bodies, 
these latter would, in continuing to circulate around the sun, 
produce all the appearances of the zodiacal Hght, without opposing 
any sensible resistance to the movement of the planets." 

To this slight sketch Laplace afterwards added some specula- 
tions as to the mechanical cause of the rotation of this nebulous 
mass, and the immediate cause of the splitting off of successive 
zones. This heated mass would in cooling contract towards 
the centre. As it contracted its velocity of rotation would, 
in consequence of one of the laws of mechanics, constantly 
increase. The time would come then when in the outer por- 
tions of the mass the centrifugal force would exceed the 
attractive power of the central portion. These outlying zones 



THE BIRTH AND DEATH OF WORLDS 413 

would then be thrown off as a revolving ring. This process 
would be repeated as the contraction continued, with the result 
of forming a series of such rings. The formerly continuous 
mass would then present some such an appearance as Saturn 
does now. 

In each of these zones the denser materials, if they existed, 
would in cooling condense first ; the zone would then be com- 
posed of mixed elements, partly solid, partly nebulous. If a 
sufficient nucleus were formed, this would gradually gather 
together unto itself all the materials of the ring, resulting in 
the formation of a fiery globe. This in further cooling would 
present us with the planets which we see and upon one of which 
we live. 

It needs be said that in the theory of Laplace, as in the 
ideas of Kant, there was much that was purely speculative. 
Moreover, the hypothesis as framed by Laplace is open to as 
serious objections as was that of Kant. It is not at all clear 
that this cooling and contraction of the nebulous mass would 
produce such zones as Laplace supposed. It was pointed out 
that with increasing rotation the mass was just as likely to throw 
off Httle wisps of vapour as a vast zone. Moreover, as Newcomb 
has pointed out, in this theory the outer planets would have 
been formed first. There seems to be no evidence that such 
was the case. It is likely that the outermost planets are still 
in a much more fluid condition than some of the inner bodies 
like the earth. Finally, the discovery of the rotation of the 
satellites of Uranus, in opposite direction to that of the other 
planets and satellites, quite disrupted the idea of perfect uni- 
formity of motion. These and perhaps other considerations, 
pointed out by various writers, forbade acceptance of the hypo- 
thesis in its primitive form. 

It needs be said, too, that the theory was never presented by 
Laplace as a finality. He gives it, he says, " with that distrust 
with which we must regard all that is not the result of observa- 
tion and of calculation." It was a conception of grandeur ; 
it had a very considerable degree of probability in spite of its 
difficulties ; it was, moreover, in its broader outlines the only 
thinkable process by which our system could have arisen. But 
had no new evidence been adduced in its favour, it would pro- 
bably have remained an interesting, not to say fascinating, 
speculation and nothing more. 



414 THE WORLD MACHINE 

A few years after the last essays of Laplace at an explana- 
tion, twenty years after the eariiest of his own, Herschel re- 
turned to the subject with fresh material for consideration. 
In two important papers he presented an elaborate theory 
showing how the ** shining fluid " of a broadly diffused nebula 
might gradually condense under the force of attraction, with 
the denser portions as nuclei or centres of attraction. The 
first stage would be a dense nebula or compressed star cluster ; 
from this would evolve one or more nebulous stars surrounded 
by an atmosphere. Finally, there would appear a single sun 
or a series of them. Leaning not upon theory but upon 
fact, he backed up his conjectures by abundant illustrations 
from the nebulae and clusters actually observable by the tele- 
scope. In a word, he adduced evidence to show that the process 
of sun formation is open to the actual observation of man. 
It is quite true that the researches of Herschel did not establish 
the Nebular Hypothesis ; it did not, moreover, attempt to 
account for planetary formation at aU ; but it did lend to the 
theory an element of objective confirmation which it had 
hitherto entirely lacked. 

But Herschel, whose genius shines increasingly with the 
years, and who seems so great to us now, must have seemed 
otherwise to his contemporaries. His daring and vivid imagina- 
tion must have excited in them some degree of distrust. Looked 
at even now, many of the results he attained seem rather the 
product of an amazing intuition than of a carefully wrought 
out induction. He had a mind which seemed to leap swiftly 
forwards to the truth. There are few of his conjectures 
— and their number was extraordinary — which have not been 
more or less completely verified by subsequent research. In 
his time he must have seemed like a prophet upon Pisgah. 

It was half a century before anything was added to the 
nebular theory as it was left by Herschel and Laplace. Then 
came considerations of an utterly different nature — indeed, 
from wholly outside the domain of astronomy. It is curious 
to reflect that it was of such a nature and such force that it 
would independently have given rise to some such a theory, had 
there been nothing else to suggest it. 

The eighteenth century was far excellence the mechanical 
century. It was the century that perfected the science of 



THE BIRTH AND DEATH OF WORLDS 415 

dynamics, that produced the steam-engine, the marvellous con- 
trivances of Vaucanson, of Droz, and many another. 

This wonderful advance inspired astonishing dreams. In- 
ventive geniuses, some of them of the highest order, laboured 
to produce mechanisms which should imitate and do the work 
of man. Some of them succeeded so well that they were haled 
before the Inquisition — not merely the makers, but the 
mechanisms — as products of the black art. A vaster and 
wilder dream was that of perpetual motion, some device which 
should give out more power than it consumed, some contri- 
vance by which the work of the world might be largely lifted 
from human shoulders. It seems fantastic to us now ; through- 
out a long period it was the constant preoccupation of many 
sane and resourceful minds. The prevailing ideas of force 
were vague ; of the present-day conceptions there were but 
adumbrations. It seemed reserved for the nineteenth century 
to clarify these ideas and to set the limits of mechanical 
possibility. 

The foundations were laid by an American. In the years 
that immediately followed the close of the Colonial Rebellion, 
a refugee from the revolted colonies, Benjamin Thompson 
(created Count Rumford) had instituted a remarkable series 
of experiments upon the nature of heat. Laplace and Lavoisier 
the chemist had jointly made an important contribution. Some 
time after, another Frenchman, a young engineer named Carnot, 
laid the foundation of the modern science of thermo-dynamics 
— that is to say, of the energy of heat. It appeared in a brief 
but very remarkable memoir, no sooner printed than straight 
away forgotten. 

It was not until the early forties of the last century that 
this solution of ideas, as it were, crystallised out. This came 
in the expression of a law something akin to that which Lavoisier 
had established as to the indestructibiUty of matter — the in- 
destructibility of energy — in Spencerian phrase, the persistence 
of force. It embodied the idea that the powers of nature, the 
forces of heat, of light, of electricity — broadly, the ability to 
perform work — represented a sum total of potential in the 
universe which remained unchanged. These forces may be 
converted one into the other : from light may come heat ; 
from heat may come the energy of steam ; from steam may 
come the motive-power to drive mills or dynamos. These 



4i6 THE WORLD MACHINE 

forces may vary in their manifestations ; no whit of their energy 
is ever lost. 

This vast idea of the correlation of forces — or, as we say 
now, of the conservation of energy — came as a veritable dis- 
covery. Like many a discovery — like, it might be said, nearly 
all great discoveries — it was reached independently and simul- 
taneously by several different minds. One of these was a rich 
brewer's son in England, James Prescott Joule ; a second was 
Colding, a Dane ; a third was Julius Robert Mayer, an obscure 
physician of Heilbronn in Germany ; a fourth was a young 
military physician of BerHn, Hermann von Helmholtz. The 
formulation of this law was in many ways the highest flight 
of the nineteenth-century mind. 

The papers in which this discovery was enunciated were 
published, each in unconsciousness of any other, between the 
years 1842 and 1847. The force of their tremendous import 
was not immediately felt. It was fifteen or twenty years before 
it seemed of enough consequence to squabble about who reached 
the idea first. But in the meantime one of its discoverers had 
seen its bearing upon the most important outlying problem 
in physical astronomy, and turned his attention thereto. This 
was the source of the sun's heat. It had long been a puzzle. 
Sir John Herschel styled it " the great secret." 

Long before this time the development of geology, the re- 
velations of the rocks, had made it clear that our earth had 
existed for aeons of time. Compared with it, the hypothetical 
date of the creation of the world did not represent the stroke 
of a second in the movements of a clock. Throughout millions 
upon millions of years the sun had been pouring downwards 
upon this ancient earth, and outwards through space, its floods 
of light and heat. Whence came this colossal store ; how 
could it thus seemingly go on for ever without diminution ? 
This was the problem, and no one could answer. 

The first to make any rational attempt was the obscure 
Heilbronn physician. Convinced by his studies that some sort 
of source must be found, unable to discover it in the sun itself, 
he thought to find it in the incessant rain of meteors upon the 
sun's face. Simple observation of the heavens had shown him 
that the number of meteorites pouring nightly and daily into 
the atmosphere of the earth was enormous. In the deep cold 



THE BIRTH AND DEATH OF WORLDS 417 

of space they are doubtless cold. In their terrific rush through 
the atmosphere they become incandescent. The amount of 
heat they develop is proportional to their speed, squared. Their 
speed is proportional to the attractive force of the earth. The 
attractive force of the sun, at its surface, is twenty-eight times 
greater than that of the earth ; the speed of the meteorites 
through the atmosphere of the sun would correspond. The 
surface of the sun is ten thousand of times that of the earth. 
The quantity of meteorites swept up by this vast body would 
be in proportion to its surface and to the force of solar gravity. 
Mayer made some rough calculations, and in 1848, in a memor- 
able paper, announced his Meteoritic Hypothesis. 

It was a noble effort ; but it did not hold. It was not long 
before it became possible to make some calculations as to the 
daily loss of the sun's energy by radiation. It is unthinkable. 
You get a glimpse of the amount from an ingenious comparison 
of Professor Langley's. He computed that if all the coal con- 
tained in the earth could be burned in an instant, it would not 
maintain the energy of the sun for one-tenth of a second. A 
similar series of calculations made it clear that a quantity of 
meteorites moving in space sufficient to keep up the sun's 
outpour of heat, would mean such a bombardment of the earth 
as to render the earth's surface red-hot. Obviously the meteor- 
itic explanation was insufficient. The mystery remained. 

Five or six years later, Mayer's compatriot, von Helmholtz, 
came forward with another explanation. By this time the once 
fluid condition of the earth, suspected by Leibnitz and Buffon, 
had been seemingly established. If the earth once existed as 
a diffused fiery mass, it would, under the influence of gravity, 
contract, just as Kant had supposed. In contracting it would 
develop heat. This heat would be radiated away into space. 
In the mind of von Helmholtz, here was the clue of the sun's 
energy : contraction. 

The mass of the sun must once have occupied millions of 
times its present volume. It must have been diffused through- 
out a space extending perhaps thousands of times beyond 
the present outermost Hmits of the solar system. By con- 
traction it has shrunk to its present proportions ; by con- 
traction is its energy maintained. This process is still going 
on. But it is evident that it has finite hmitations in time. 
The mass of the sun is known ; the amount of contraction 

2 D 



41 8 THE WORLD MACHINE 

needful to develop its annual expenditure of heat can be cal- 
culated. Relative to its mass this amount is small ; two or 
three hundred feet per year, a few miles per century, would 
suffice. It would be long before such a contraction would be 
evident to any human measures. In six thousand years it 
would lessen the apparent size of the sun to us by less than 
a second of arc — that is to say, by less than an i8ooth part of 
its present angular size. 

This is slow ; but it is unceasing. Upon the calculations of 
von Helmholtz and others who followed him, it could scarce 
have been going on, at its present intensity, for more than 
eighteen or twenty millions of years. Moreover — and this was 
the startHng feature — the process is nearing an end. If the 
total available supply which the contraction of the sun's mass 
could produce were divided into 454 parts, Helmholtz cal- 
culated that 453 of these parts had been spent. He pictured 
the solar mechanism as a kind of clock which was run down. 
Some day or other it would cease — on present-day calculations, 
within a period of something like seven millions of years. 

It is needless to say that these estimates excited the liveliest 
interest, even among the laity. By some twist of chance, 
von Helmholtz' s conclusions were made public in a popular 
lecture delivered at Konigsberg, the home of Kant, whither he 
had gone to occupy a chair of physiology. They were presented 
as an incident in an exposition of the new theories of energy ; 
the lecture was entitled ** On the Interaction of Natural Forces." 

Von Helmholtz's ideas were vehemently attacked. The con- 
clusions of the geologists demanded, even for the events upon 
our little earth, a bank account of time compared with which 
seventeen million years was a bagatelle. The intrusion of the 
physicist was hotly resented. The new ideas found a valiant 
exponent in the sturdy figure of young WiUiam Thomson, now 
our distinguished Lord Kelvin. He has done many a battle in 
their defence. In later years Lord Kelvin has shown an in- 
clination to modify — that is to say, enlarge — the estimated 
allowance. Even stretching it to the utmost, it still seems 
insufficient. The explanation of one mystery seemed only to 
substitute another hardly less acute. It is possible that, within 
the last year or two, the faint beginnings of our knowledge of 
radium and radio-activity offer a gleam of explanation and 
perhaps conciliation. It is too soon to be sure. 



THE BIRTH AND DEATH OF WORLDS 419 

In their main features, after half a century, von Helmholtz's 
conclusions remain unshaken. They do not exclude the con- 
tribution of the meteorites. If radio-active bodies exist in the 
sun, they too may share in the sun's support. But the main 
source of its vast wealth of heat and light is the contraction of 
its own mass. The power to which Kant and Laplace had 
attributed the origin of the solar system has likewise dowered 
it with warmth, with Hght, with hfe. 

But the matter of especial interest here is the support which 
the theories of solar energy have given to the Nebular Hypo- 
thesis. Newcomb has pointed out that Kant and Laplace 
reached their conceptions in some sense by reasoning forwards 
— that is to say, they assumed that a nebulous mass once 
existed. There was no proof of this. They reasoned by a 
process of deduction. The path followed by Helmholtz was 
the reverse — he reasoned backwards. His results were attained 
by an induction from observed facts. He showed that, work- 
ing back from present conditions, we should inevitably reach 
precisely such a condition as his forerunners had assumed. 
That two opposite modes of reasoning from utterly different 
sets of facts should have thus led to an identical result, gave 
to the hypothesis a solidity of foundation from which it can 
in no probability be shaken. Whatever may be the details of 
planetary evolution, the main fact was now clear. 

Something Hke finahty and, with it, some highly suggestive 
indications were brought by the camera. When the eager, 
searching eyes of Herschel had closed their long scrutiny, the 
number of known nebulae had reached 2500. With the aid of 
the camera, the number estimated as presently known is above 
120,000. Utilising the great Crossley reflector at the Lick 
Observatory, the late Professor Keeler, whose researches in 
this field disclosed so much that was new, was able to calcu- 
late that the total number which the camera might eventually 
record would reach several hundred thousand. In a word, the 
universe is teeming with them, and their extent is beyond con- 
ception. They are for the most part so distant that they have 
no observable parallax. Yet some of them range across several 
minutes of arc in the telescopic field. It follows, therefore, 
that some of the nebulae must be thousands of times in extent 
the diameter of the earth's orbit. Probably a great number 



420 THE WORLD MACHINE 

of them are thousands of times the dimensions of the whole 
solar system. In other words, present-day telescopes, in com- 
bination with the photographic plate, reveal the objective 
existence of precisely such masses as the hypothesis had 
required. Let us clinch the point. 

In some of the older works at least, the ideas of Kant and 
Laplace are rather scantily dismissed as a mere hypothesis, 
** interesting if true." We now know that diffused masses of 
unthinkable extent do exist. The theory of solar energy and 
of a once molten earth show that such masses must have 
existed. The especial characteristics of our solar system in- 
dicated the same thing, and pointed out the probable course 
of planetary evolution. It would seem as if no further proof 
were needed ; yet further proof exists. The camera has seemed 
to reveal that some such a process as Kant and Laplace sup- 
posed is actually taking place ; not in a single instance nor 
as an isolated phenomenon, but throughout the whole course of 
the heavens. 

Herschel's reflector was four feet in diameter. When it was 
first built it seemed little less than a miracle of ingenuity. It 
was hardly less a miracle of human patience. A quarter of a 
century after Herschel's death, and after many unsuccessful 
experiments. Lord Rosse succeeded in constructing, at Parsons- 
town in Ireland, a reflecting telescope with a six-foot mirror 
and nearly sixty feet in length. Its *' light grasp " was more 
than double that of Herschel's. It was with the aid of this 
beautiful instrument that Lord Rosse disclosed for the first 
time the existence of spiral nebulae — that is, nebulae showing 
some such a spiral disk that is seen in the little St. Catherine's 
wheels. Some of his drawings were of exceeding beauty. It 
was a discovery of the first significance ; but he was an ama- 
teur and a lord. It is to the discredit of academic astronomy 
that for a long time Lord Rosse's observations were ignored. 
Later on, out of an estimated 120,000 nebulae, Professor Keeler 
could calculate that more than half, possibly nearly all, show 
this spiral shape. 

It is in the highest degree improbable that this appearance 
is a mere chance. There seems no escaping the conclusion 
that these spiral nebulae are in rotation, just as the nebular 
theory requires. 

There are other appearances which at least suggest a way by 



THE BIRTH AND DEATH OF WORLDS 421 

which this rotatory motion might have been acquired, and 
perhaps shed some Hght upon the modes of planetary formation. 
Some of the more distinct nebulae appear to show knots or 
clumps of denser formation, as though they in no wise possess 
a uniform constitution, but that within the mass several centres 
of condensation have begun to appear. 

We have just a hint as to how these centres or nuclei might 
be formed. We know on the one hand that the number of 
nebulae is enormous ; on the other hand, that space is simply 
teeming with meteoritic or cometary swarms. These range in 
size all the way from grains of sand and brickbats up to bodies 
of considerable magnitude. When after uncounted aeons a 
nebula had become somewhat thickened, if it were then to 
encounter a meteoritic swarm, it might readily arrest the motion 
of the latter and imprison it within its meshes. The motion 
of the meteorites would be partly dissipated in heat, partly 
in imparting motion to the nebula itself. It is conceivable 
that if such a swarm were very great, and the nebula already 
of some density, this might give rise in time to just the ap- 
pearances which we perceive. 

It may be that this imprisonment of meteorites within the 
spider-web of the nebulae is no isolated event, but that it is a 
continuous process, like unto the sweeping up of the meteorites 
by the earth, the sun, and other large bodies. We know that 
some of the nebulae at least are in very rapid motion, at speeds 
quite comparable to that of the stars themselves. It is very 
easy to suppose that they would of necessity encounter vast 
quantities of meteors. 

Occasionally they would encounter a sun. It may be that 
this explains the blazing up of " new " stars, now a well- 
recognised fact of stellar observation. In whatever way these 
centres of condensation may form, it is easy to see that by 
further condensation, they might readily result in the ring- 
like or Saturn-like appearances which some of the nebulae 
present. If this were true the difficulty of understanding how 
these zones or rings were formed by the condensation of a nebular 
mass would be dissipated. 

Moreover, it may be that the mode of evolution is not 
single, but that the process varies considerably under varying 
physical conditions. Still there is unmistakably in nature a 
certain unity. The modes of reproduction of life, whether of 



422 THE WORLD MACHINE 

plant or animal, are at basis the same, though they differ widely 
in their details. A certain general analogy leads us to suppose 
that a like basic unity, with no doubt the same incidental 
variety, obtains in the reproduction of worlds. There seems 
no reason now to doubt but that the general features of the 
life-history of suns and systems is known. 

When we consider the ineffable littleness of man and his 
world, this is a prodigious step. That he should be able to 
gain a sweep through such ranges of cosmic space and time 
seems almost weirdly incredible. Yet is he not satisfied, yet 
will he still go on. The earth was once a part of the sun, the 
sun was once a diffused fire-mist. It is thus that systems are 
born. But whence comes the fire-mist — what are these nebulae ? 

Until very recently the general supposition was that these 
nebulae represented a primal matter, the urstoff of the elements, 
and that perhaps by a process of condensation the various 
elementary substances which are found upon the earth were 
formed. The revelations of the spectroscope seem to negative 
this view. It is not impossible that the analogy noted above 
may be carried yet further. Through a series of hesitating 
approximations, biology reached at last the conception that 
the round of the matter of life is eternal and unceasing. The 
fact was expressed in the dictum, omne vivum e vivo. It is 
possible that much the same is true of the universe. Moreover, 
throughout cosmos we may discover the same process of dis- 
solution and death that we find in the world of life. 

Shortly after the doctrine of the conservation of energy had 
been established, Lord Kelvin filed notice that account must 
be made of its dissipation as well. For example, so far as our 
little solar system is concerned, the idea of conservation would 
be a monstrous joke. The colossal energy of the sun is not 
conserved at all. It is wasted with a prodigaHty compared 
with which the most riotous spendthrift would seem a miser. 
If Mr. Rockefeller or Mr. Carnegie were to melt up their gold 
into bullets to shoot rabbits with, if they were to make bonfires 
of their bonds, they could not throw away their wealth more 
recklessly than does our central solar magnate. The quantity 
of warmth and light taken up by the planets is of course not a 
billionth part of that which is radiated away into space. 

In the course of time, then, the sun will grow dark and 



THE BIRTH AND DEATH OF WORLDS 423 

cold, life upon the planets will no longer be possible ; our 
system will be simply a series of revolving icicles. This pro- 
bable fate seems already that of millions of others. It is a 
disclosure of recent years that the universe is full of dark suns. 
Half a century ago we knew of none at all. Now we must 
believe with Arrhenius that the number of dark suns far exceeds 
the number of those that blaze. 

It follows from this fact of dissipation that in the course of 
time all the suns now lighting the heavens will one day go out. 
So we might picture the universe, originally dispersed in nebulae, 
gradually gathering itself together into clumpy aggregations, 
these in turn condensing into suns and glowing planets, eventu- 
ally to sputter and go out, then whirl on in icy immobility 
throughout the endless years. The picture is not inviting. To 
most minds it is dispiriting. We have no need to suppose it 
is true. 

In any account of creation we must take note of the new 
stars that blaze out into the heavens and show for a little, then 
disappear or sink back into obscurity. Originally it was sup- 
posed that these apparitions were rare ; we have seen that 
they are probably of frequent occurrence, and that in some 
instances at least they result from the collision of two suns. 
Their motions accelerated by their mutual attraction, they 
would approach each other with frightful velocities. If they 
struck the crash would be terrific. The amount and the degree 
of heat generated by the impact of two vast bodies would be 
such as utterly to dissipate them into vapour. They would be 
diffused again into the primal fire-mist from which they sprung, 
slowly to cool through the ages, slowly to grow hot again through 
their contraction and coalescence. 

It is from the crash of suns, then, that the nebulae may come. 
This is their origin, and this is the round of cosmic life. So at 
least, so far as our present knowledge extends, must we conceive 
it. It is thus that the cosmic process is sketched in the brilliant 
pages of Arrhenius.^ 

In this view the basis of the elements, the substance of the 
universe, is eternal, likewise the process which it pursues. A 
new Moleschott might now write a Kreislauf der Materie, a 
Circulation of Matter. Devolution follows evolution, regenera- 
tion follows degeneration, world without end. 

1 Lehrbuch der Kosmischen Physik, Leipzig, 1902. 



424 THE WORLD MACHINE 

The process has obviously three stages — the nebular period, 
the star period, the dark sun period. The duration of these is 
not coequal. In the estimation of Arrhenius, the nebulous stage 
is vastly the longest. Next after that would come the dark 
sun stage ; conceivably this might last for a time which, so 
far as our human imagination could compass it, would seem 
infinite. A rushing star might pursue its path through the 
heavens for ages without meeting with another, in the union 
with which it might be again scattered to fertilise the ways of 
space. Yet it is evident that with anything like an average 
distribution of stars through space, there would be an average 
chance of impact. Therefore there would be a general average 
for the period of darkness, as there would be a like average term 
for the period of nebulous diffusion. 

The period of solar activity, of what we might term solar 
life, is comparatively easy of computation. In a rough way we 
already know this period for our own sun. It is easy to see 
that this period is but an incident, a few seconds, or at most 
minutes, perhaps, in the arc of this unceasing circle. Just as 
life appears an inconsequent moment in the evolution of the 
stellar system, so the term of solar brilliancy, which alone makes 
this moment of human being possible, is itself but a slender 
fraction of the larger life of the stars. 

It seems as if we may at last make answer to the inquiry 
of Epicurus : " And whence came chaos ? " Apparently chaos 
comes from the cosmos, as the cosmos in its turn comes again 
from chaos. In this view there was no chaos, no beginning, 
and there may never be an end. It is conceivable that the 
universe — that is to say, the universe of suns and worlds to 
which we belong — has a finite limit in space, though to space 
itself the mind may set no bounds. But limits in time for 
the vast swarm of systems which the telescope brings in view are 
difficult to perceive. It seems to be a ceaseless turning of a 
wheel. 

But there remains always the unceasing dissipation of energy. 
It may be as Arrhenius pictures it, that when a sun has cooled 
sufficiently to form a crust, it will conserve practically the whole 
of its heat through a vast period ; it would dissipate less in 
hundreds of thousands of years then than in a single year now. 
It may be, too, that the energy radiated away into space from 



THE BIRTH AND DEATH OF WORLDS 425 

a billion suns is eventually absorbed by billions of nebulae. But 
in the end, if the universe is finite, some loss must take place. 
Even though its clock hands move so slowly that the duration 
of our whole solar system might represent the flash of a falling 
meteor, still in the ultimate view it is difficult to conceive the 
round of cosmic life as a perfect circle, without a diminution and 
without a break. 

Sometimes among scientific workers one perceives a certain 
arrogance, as though the great problems of existence had been 
quite disposed of. Doubtless it is a consequence of that foolish 
academic spirit engendered by long contact with only young 
and immature minds. It is hard to realise that the development 
of the mind under rigorous methods of proof is only just begun. 
Few of the larger problems have yet been touched. Of the fate 
of cosmos we can know little until we know more of what cosmos 
is composed. 

The spectroscope has told us much. What must we infer 
from the newer knowledge that has come within a few years ? 



CHAPTER XXXII 

THE COSMIC EXCHANGE OF MATTER 
AND LIFE 



Worlds on worlds are rolling ever 

From creation to decay, 
Like the bubbles on a river. 

Sparkling, bursting, borne away. 

Shelley, Hellas. 



Our little systems have their day, 
They have their day and cease to be. 

/u Memoriam. 



CHAPTER XXXII 

THE COSMIC EXCHANGE OF MATTER 
AND LIFE 

When, after so many centuries of prediction and expectation, 
the New World was actually found, Europe could not rest for 
thinking its full of wonders, as men had dreamed so long. The 
persistence of this belief seems curious now. Nowadays the 
trained imagination of the scientific adventurer has no such 
expectations of the unknown. There may be some 'witless folk 
left still to beHeve that if we could reach the North Pole we 
should find griffins and goblins and giants and genii. What the 
four hundred intervening years since Columbus have taught us 
mainly is the art of accurate inference and prediction. We can 
foretell what the polar regions are like, and we know them to 
be destitute of any sane man's interest. Can we form any idea 
of worlds outside our own ? 

If it should turn out that the stellar universe has no more 
real " structure " than that of a gas — if the resemblance to the 
kinetic theory of gases which I have suggested should be veri- 
fied, the fact would carry with it many interesting implications. 
One of these would be the incessant exchange — incessant at 
least in the sense of cosmic time — of the material and of the 
units of which this universe is composed, perhaps of life as 
well. This could but mean the ultimate identity of the world 
scheme throughout the farthest reaches of space. 

If we follow the analogy of the kinetic theory, we must 
either conceive of the number of dark suns or dark bodies as 
very great, or else picture the universe cLS a gas which is very 
thin. The molecules of the air which we breathe, for example, 
are not spaced at anything like the distances which we at pre- 
sent regard as the average spacing of the suns. When the air 
is reduced to a liquid or frozen solid, or what is very nearly 
the same thing, when water goes over into vapour or steam, 
the difference of the volume occupied is not enormous. A cubic 



430 THE WORLD MACHINE 

inch of water produces only about 1800 cubic inches of steam at 
ordinary pressures. 

Water is practically incompressible, and we must therefore 
conceive the molecules of which it is composed as in practical 
contact. In a state of vapour, then, according to the kinetic 
theory, the molecules are distant one from the other on the 
average about 1800 times their own diameters. 

With the perfected air-pump it is possible to reduce the rare- 
faction of a gas to less than a millionth of its density at ordinary 
pressures. By means of liquid air this may be carried somewhat 
farther. In a gas at this density we may conceive the molecules 
then as eighteen million times and more their own diameters 
apart. If the distance between alpha Centauri and our sun re- 
presents anything Hke an average spacing of the stars, then, 
pursuing our conception of the universe as a stellar gas with the 
molecules as suns, its density would be something like air or 
water vapour at less than one-millionth atmospheric pressure. 

If we conceived of a thousand dark suns for one blazing 
star, this stellar gas would still be highly rarefied as compared 
with ordinary air. It would still be exceedingly tenuous if we 
conceived of a million dark bodies for every luminous sun. It 
is almost impossible for balloonists to survive when the baro- 
meter has dropped two- thirds. If, then, the imaginative Mr. 
Wells were to write a story whose characters were vast beings 
breathing this stellar air, he would have to picture them as able 
to exist in a much more ethereal medium than those which live 
and move about at the bottom of our sea of earthly atmosphere. 

But if the stars were spaced on the average of thirty million 
times their own diameters, the chances of collisions between 
suns would be almost infinitely small. It would probably not 
begin to account for the number of new stars which blaze forth 
in the sky. It is possible, of course, that a simple rush through 
a relatively dense nebula might account for many of these; 
probably l^not all. The number of dark bodies must therefore be 
considerable. Analogy with known suns like Sirius, Arcturus, 
and Canopus would suggest many of them are of colossal size. 
Even when they are cooled down to the crust-forming stage the 
energy they contain is still prodigious. We conceive the interior 
of the earth as a glowing gas practically rigid under the enormous 
pressure which it sustains. We may believe this true of all dark 
bodies, large and small. 



COSMIC EXCHANGE OF MATTER AND LIFE 431 

It follows that even a relatively small body crashing through 
the enclosing crust would produce a terrific eruption. When a 
pair of bodies comparable in grandeur with the sun came 
together, the effect of course would be tremendous. It would 
resemble an explosion, and the matter they contained would 
be blown about over an area that would be considerable, 
measured even by stellar spaces. If this process were continued 
over extended periods of cosmic time, the result would be a 
more or less even distribution of the different materials or 
elements of which the suns are composed. It would produce 
precisely the condition of more or less kinship of constitution 
which the spectroscope has revealed. 

It is evident that the number of relatively near approaches 
of the suns would be immensely greater than the number of 
actual collisions. If we conceive the suns in general as pro- 
vided with satellites like our own, the effect of this nearing of 
the suns would be a constant planetary exchange. Thus, for 
example, suppose that our sun and alpha Centauri should come 
rather closely together, they might not collide ; they might be 
moving too swiftly to form a binary system. They still might 
approach near enough so that our sun would rob alpha Centauri 
of an outer planet or so, or alpha Centauri might rob our system 
of Neptune or Uranus. 

Lively minds may, if they Hke, picture the stellar dance 
as a sort of endless Virginia Reel, with the suns flinging 
off their partners and taking new suns in a continual round. 
Just as we conceive the particles of musk or the particles of 
smoke diffusing through the air of a room perforce of the in- 
cessant movement, collision, and rebound of the particles of air, 
so we might in imagination portray the planets as diffusing 
through space, going on from one sun to another, to the end of 
the world. The cosmic processes are leisurely ; but time is long. 

In yet another way the binary systems might easily lose their 
satellites simply by means of their mutual attraction one upon 
the other. It is easy to see that when a planet or satellite 
swept between a pair of suns, its orbit would be straightened 
out more or less, with the result that the planet would pursue a 
path extremely elliptical, or else go shooting away into space. 
With a speed sufficient, they would of course go travelling on 
until they came within the sphere of influence of another system.^ 
» T. J. J. See, The Evolution of Stellar Systems. 



432 THE WORLD MACHINE 

We have never run across as yet such a runaway planet, 
nor have we any actual evidence that they exist. But the 
possibility is one of the plain implications from our recently 
acquired knowledge of twin suns. For aught we know this 
may be the origin of one or more of the planets of our own 
system, though the striking uniformity in all the motions of 
our system makes the chances against this perhaps millions to 
one. It is difficult to understand how a planet coming, on the 
theory of chance, from any one of the possible directions of 
space could be swung into line into the general plane of 
planetary motion and set marching with the rest, all by the 
sheer power of gravitation. 

Be this as it may, the apparent conclusion which we may 
draw regarding the stability of our planetary system is precisely 
the opposite from the conclusions of Laplace and Lagrange. So 
far as the motions and forces inherent to it are concerned, our 
system would apparently be stable throughout infinite ranges 
of time. For anything that we can now perceive this is the 
case. But the probability that the vast majority of heavenly 
bodies are not luminous but dark, the consequent implication 
of great number and increased possibility of approaches and 
collisions, gives the matter quite another aspect. In another 
two or three hundred years perhaps we shall know something 
of the actual number of bodies in space, perhaps of their rela- 
tive separation as well. Then it would be possible to compute, 
on the theory of probability, the average chance which every 
system has of surviving amid the constant clash of the suns 
as they pursue their interweaving ways. 

How many of the meteoric swarms through which the earth 
sweeps are of origin foreign to the solar system we do not know. 
Quite possibly all of them are ; it is fairly certain that some of 
them are. We have seen our globe and all of the other planets 
sweeping up hundreds of tons of them per day, the sun possibly 
thousands of tons. We have, then, in the meteoric showers a 
steady cosmic contribution to the mass of our system. On the 
other hand, the far larger part our system may act simply 
as a temporary carrier ; we may be steadily picking up swarms 
as we push through space. These swarms take on highly 
elliptical orbits ; in nearing another system these might be 
much more readily shed than a planet. In the same fashion 
we might Hft a few swarms from some neighbourly sun. 



COSMIC EXCHANGE OF MATTER AND LIFE 433 

It goes without saying that what is true of the meteors is 
equally true of comets, since, as we have seen, they are pro- 
bably one and the same thing. By whatever name we know 
them, the result is a constant addition to every considerable 
body of our own system, a steady taking up of cosmic material, 
accompanied doubtless by a constant levy upon our system as, 
through the long ranges of time, we come within the attractive 
sphere of some dark or luminous sun. 

This unending exchange of matter and its larger aggregations 
which we thus may picture, is not the sole way that the materials 
of the universe might be equaHsed. There is another that is 
probably going on under our eyes. It involves the infinitely 
little as the other may engage the almost infinitely large. This 
is the incessant radiation of particles from all incandescent 
bodies. 

A candle, the arc of the electric-light, the sun too, probably 
— in brief, everything which glows is sending into the space 
about it a shower of minute corpuscles of ultra-atomic dimen- 
sions. Moreover, and quite independent of this, aU highly 
luminous bodies, and in especial the sun, are constantly driving 
from them minute particles of matter under the, pressure of light. 

Nothing at first seems stranger than that the immaterial 
sunlight might exert a propulsive force. It is hard to think 
that as it drives against the earth and other bodies it bears 
down upon them with a certain energy. It was indeed a logical 
inference from the ether- wave theory of radiation. Professor 
Clerk Maxwell, who pointed out this necessity, mathematically 
developed what this light pressure or force must be. He had a 
rare combination of the mathematical — that is, the essentially 
analytic — and the constructive or synthetic mind. In this 
problem and in another he illustrated one of the astonishingly 
rare instances in which mathematics has ever pointed the way 
to scientific discovery. 

It is only two or three years ago that a Russian physicist, 
Lebedeff, and almost simultaneously Nichols and Hull, in 
America, by experiments of exceeding ingenuity, demonstrated 
the existence of this pressure. It is extremely slight ; but it is 
to be noted that the force it exerts will be in proportion to the 
surface of the body upon which it acts. On the other hand, it 
is evident that the powers of gravitation are in proportion to 

2 E 



434 THE WORLD MACHINE 

the mass of bodies. This has a curious consequence. The mass 
of a body decreases in proportion to the cube of its diameter ; 
but the surface decreases only in proportion to the square. It 
follows, therefore, that with smaller and smaller bodies the re- 
lations between the force of attraction and of light pressure 
progressively alter ; gravitation decreases much more rapidly 
than the force of light. It is evident, then, that there will come 
a point where the pressure of light is actually greater than the 
pull of attraction. At this point the particle has become ex- 
ceeding small ; but it will then be shot away from a highly 
luminous body, even against the tremendous gravitational pull 
of the sun itself. 

This critical diameter, as it is termed, is reached with particles 
less than a micron and a half thick, supposing them to have the 
same density or specific gravity as water. A micron is the 
o-j-J-o^th part of an inch. The speeds which may be thus im- 
parted to these particles are something enormous. A micro- 
scopic body of matter of half the dimensions indicated will dash 
from the sun at a rate of 500 kilometres per second. One 
might imagine that with a constant decrease of the size of the 
particle this speed might become practically infinite. As a 
matter of fact it has a hmit, which is perhaps eighteen times 
500 kilometres ; that would be 9000 kilometres, or upwards of 
5000 miles, fey second. At such velocities a particle shot from 
the sun would reach the earth after a few hours. 

The consequence of this pressure of Hght we are only just 
beginning to perceive. To be sure, the quantity of matter in- 
volved is extraordinarily slight. On the other hand, the out- 
pour is enormous. Und die Zeit ist unendlich lang. It is an 
ingenious suggestion of Arrhenius, from whose paper these 
interesting details are drawn, that we may have here the solution 
of one of the outstanding riddles of cosmical physics. Perhaps 
this is the origin of the meteorites. 

It is very striking that the meteorites seem to consist of 
minute particles in relatively loose combination. They are 
rather porous, and seem to be built up particle by particle. 
When they are melted down the result is a solid and vitreous 
mass, a very different substance from the pumice-like meteorite 
which reaches the earth. In their wanderings through space 
we may conceive these particles coming into collisions sufficient 
lightly to fuse them together. Once such a nucleus was formed 



COSMIC EXCHANGE OF MATTER AND LIFE 435 

it would possibly continue to grow and grow. Large bodies 
might thus be built up. 

If this be the secret of the meteorites, and the meteorites in 
their turn are the nuclei of planets and suns, we possess then a 
complete picture of the round of the cosmic exchange. We 
perceive that there is in the universe nothing constant, nothing 
stable. There is incessant motion, incessant aggregation, in- 
cessant disaggregation. Conceivably in the coming years the 
advance of our ultra -physical knowledge will give us an insight 
into the creation and the concomitant annihilation of what in 
our present ignorance we term matter. 

Not a little in the recent extensions of physical theory, at 
the hands of Professor J. J. Thompson, Sir William Ramsay, 
Rutherford, and their co-workers, suggests that the problem of 
the creation and annihilation of matter is not transcendent, as 
up to three or four years ago it was supposed to be. The para- 
doxical performances of radium, the general phenomena of 
radio-activity as well, indicate that the process may be in- 
cessant, and furthermore observable ; what is still more, that 
its fuU deHneation is at hand. 

This conceivable creation and dissipation of matter would 
be then, in our present phraseology, a function of energy. The 
cosmic exchange of matter, alike in large masses and in very 
small, would be in larger view but a part of that cosmic exchange 
of energy which was a commonplace before more than the 
vaguest conceptions of energy had been framed. To the most 
primitive mind it was evident that every form of earthly life, 
vegetable alike as animal, was in some sense progeny of the 
sun. Possibly we may widen the conception to look upon the 
sun and aU its myriad kind, as in some sense centres of projection 
of a creative energy whose evanescent manifestation is that 
material world in which we live and part of which we are. 

Our account of the universe in terms of substance and force, 
the irreconcilable and unescapable antinomies of our human 
thought, would then be closed. Aside from the ever-interesting 
details of their interworkings, there would be nothing left for 
speculation save the everlasting and implacable inquiry of 
Voltaire — doubtless, too, of the Voltaires of thousands of years 
gone — his ironical and impertinent — 

** Why is anything ? " 



436 THE WORLD MACHINE 

We may picture a cosmic interchange of the material of 
shattered suns, the stuff too of all the glowing suns ; an inter- 
change as well of planets, conceivably with their contents quite 
intact. May we go yet further and picture a cosmic interchange 
of hfe ? 

The problem of vital origins has been coeval almost with that 
of the origin of the world. Considering the amount of acrid 
controversy, alike theological and scientific, which it has en- 
gendered, one might also say that it has been co-evil. 

When the architectonic theory of creation was given up, the 
Chaldeans' entertaining tales of life's beginnings went with it. 
With the discoveries of the microscope it seemed possible to 
pursue forms of life almost to molecular dimensions, and from 
this it did not seem absurd to suppose that, under favouring 
conditions, the activities which we call vital might be spon- 
taneously set in motion. It was the service of Pasteur and his 
kind to show that, whatever may have been true of the past, 
we have no evidence that spontaneous generation takes place 
now. As the chemist could get no further than the micro- 
scopist, speculative minds were not wanting to imagine the origin 
of life from ultramundane sources. 

This suggestion came from two of the strongest heads 
anywhere to be found within the last half-century. One of them 
was the latter-day leader of English physicists whom we know 
as Lord Kelvin ; the other was the multi-minded von Helm- 
holtz, almost equally distinguished as physicist, mathematician, 
and physiologist. Independently, each of them conceived that 
life may have never originated upon this earth at all, but that 
it might have been brought to our planet through the agency 
of meteorites. They imagined that germs from distant worlds 
might have been tucked away in the interstices of meteoritic 
stones, and reaching the earth, have found here a favourable 
medium. From this might have come all the myriad wonders of 
life after the manner revealed in the latter-day Gospel According 
to Darwin. 

It is curious that a speculation — it was never anything more 
— deriving from two minds so eminently sane and unfanciful, 
should have met with such a show of disaffection as this un- 
doubtedly did. It was objected that in its rush through the 
atmosphere, as a shooting-star, the meteorite develops a tem- 
perature probably of several thousand degrees, and that all 



COSMIC EXCHANGE OF MATTER AND LIFE 437 

possible life would thus be simply annihilated. The objection 
was not in the least valid. It is now known that in the brief 
moment of its flash through the air only the surface of the 
meteorite is fused ; when the interior temperature can be 
measured soon after its fall to the earth, it is found to be 
astonishingly cold, just as our supposition regarding the cold 
of space would require. A much more serious difficulty lay in 
our later-gained knowledge of the meteorites themselves. It 
is not at all clear that they are chips of shattered planets from 
far-off systems. 

But in the suggestive paper already referred to, Die Ver- 
breitung des Lebens in Weltenraum} Arrhenius has given this 
extramundane theory a new and very plausible form. The 
distinguished Swedish compeer of Kelvin and von Helmholtz 
points out that we already know of life-germs less than a 
quarter of a micron in diameter ; and since there exist several 
bacterial diseases wherein the germ is apparently too small for 
microscopic detection, we may suppose other germ forms yet 
more minute. Smaller still must be their spores or seed-like 
granules, with resistant envelopes, which the bacteria throw 
off, and to which their continued existence is due. 

Many of the bacteria we know float in the air ; so much the 
more must the spore germs. It is easy to see how they might 
be carried up by air-currents into the higher levels of the 
atmosphere. It is Arrhenius' interesting suggestion that from 
there they might be driven off into space perforce of electrical 
repulsions. 

It has been for a long time known that the earth possesses an 
electrical " charge," that bodies or particles will be attracted to 
or repelled from it just as, let us say, bodies of paper are 
caught up by a glass rod when the rod is rubbed up smartly. 
The globe is in a way a vast electrical '' field," which by times 
— say, upon a clear, snappy winter morning — may attain con- 
siderable intensity. 

We have come in later days to know that there is a unit of 
electrical charge, or, as we might say, an electrical atom. When 
a body is " electrified " it is, as it were, covered with these 
electrical atoms. This unit charge may be sustained by very 
minute bodies as well as by larger ones. It is not a function of 
surface or mass. It foUows, therefore, that we may conceive of 
^ Die Umschaii, June 13, 1903. 



438 THE WORLD MACHINE 

charged particles so small as to be repelled by the negatively 
charged earth with greater force than the puU of gravitation. 
Arrhenius computes that a particle one-seventh a micron in 
diameter, possessing a unit charge, might be driven off and out 
of the earth's atmosphere by this means. 

A seventh of a micron is about the size of the smallest 
bacterium known. We have life particles, therefore, of the 
requisite minuteness. But how could they acquire an electrical 
" charge " ? Arrhenius answers : from the sun. The particles 
shot off from candescent bodies bear always a negative electrical 
charge. The sun, we know, is raining these cathode particles or 
corpuscles into space in every direction. The earth is rushing 
through a continuous if imperceptible hail of them. It is the 
beating in and union of these solar corpuscles with the particles 
of air in the upper strata of the atmosphere which probably 
explains the appearance of the polar light. 

These corpuscles could just as well unite with a germ or a 
spore as with a particle of water or of air. They are of ultra- 
atomic mass. They would add practically nothing, therefore, 
to the weight of the germ or spore, while they would impart to 
the latter their electrical charges. In the outermost strata of 
the atmosphere the free-path motion of the air molecules may 
be rods or even miles wide ; the germs would encounter no 
retaining force to hold them in leash ; they would go travelling 
out into the void, where they would come under the impulsion 
of the pressure of light. Arrhenius calculates that a germ of 
this size would be driven at a speed sufficient to carry it to the 
nearest of the fixed stars in three thousand years. 

We may conceive of yet another rate of transport than that 
suggested by Arrhenius. We have seen that space is swarming 
with meteorites ; the spores might readily be caught up in a 
meteoritic stream and be carried onward to far realms of stars. 
The germs might easily become embedded in the growing bodies 
of the meteors, and thus they might penetrate the atmosphere 
of another planet with the latter. We should have then a 
realisation of precisely the conditions imagined by Kelvin and 
von Helmholtz. 

It might readily be objected that no germ or spore is known 
capable of retaining its vital energies for so long a period. But 
a germ or spore in its travels would be subjected to the tempera- 
ture of space, and this we estimate at but a few degrees above 



COSMIC EXCHANGE OF MATTER AND LIFE 439 

absolute zero. The effect would be precisely the same as if 
they were frozen in solid hydrogen. The vital activities are 
simply a function of temperature, and at this intensity of cold 
they practically cease. Dr. Allen Macfadyen, of the Jenner 
Institute in London, has shown that germs and spores may be 
subjected to this infra- freezing process without being " killed." 
They resume their activities, pernicious or otherwise, when they 
are thawed out. 

Let us conceive that these frozen germs or spores reach 
another planet whereon no life whatever exists. All of the same 
material, the planets probably all follow more or less the same 
course of evolution. So soon, then, as they have cooled off 
sufficiently from their glowing state to form a crust, they con- 
stitute a possible milieu of life. It is reasonable to suppose that 
as soon as the heated vapour of these hot planets has condensed 
to water, and a carbonic acid-laden atmosphere is formed, the 
lowest forms of plant life, the bacteria, may thrive and develop. 
It is known that some forms at least can sustain a temperature 
of 90° C. or very near to the boiling-point. 

This is the kernel. Once it is planted upon a cooling globe, 
we may readily conceive the latter to become the theatre of such 
a wondrous vital activity as that which in aeons gone our earth 
has been the scene. 

It is perhaps worthy of note that the idea of a cosmic dis- 
tribution of the elementary forms of life adds nothing to, as it 
subtracts little from, the mystery of life itself. It in no wise 
precludes the possibility of spontaneous generation upon the 
earth or elsewhere, incessant or sporadic, now or at some distant 
anterior time. It in no wise precludes the possibility of the 
production of life in the laboratory. It may be a fact that no 
such thing as spontaneous generation has ever taken place upon 
the earth. It is even conceivable that it has never taken place 
historically within the cosmos. The peculiar molecular com- 
plication which displays the phenomena of life may be co- 
existent in time with the universe itself. Such seems more or 
less the view of Arrhenius. 

Be this as it may, we have no more present reason to infer 
this than to suppose that sulphide of iron, or some other more 
or less complex inorganic compound, was never formed syn- 
thetically upon the earth. Sulphides and other compounds are 



440 THE WORLD MACHINE 

found widely distributed over the earth ; they hkewise occur 
in meteorites, conceivably also in meteoritic dust. Some of 
these compounds may exist in the minute particles which reach 
the earth under the pressure of radiation. Probably it would be 
very difficult to find anjrwhere upon the earth an actual synthesis 
of these compounds now taking place. Yet there is no mystery 
about them. They are formed and unformed, daily and hourly, 
in the laboratory and in industrial processes. We have, more- 
over, excellent reason for supposing their natural production 
at some period or other of the earth's history. In brief, a given 
substance that one might pick up in the street might have been 
produced by a chemist ; it might have been formed when the 
earth was at the temperature of a blast-furnace ; it might have 
come from some celestial stithy at ten million times the distance 
of the sun. 

So with Hfe. Forms of life may reach us in one way and 
another from every part of the universe ; but at the same time 
its spontaneous production from inorganic materials may be 
taking place on the earth without cease, let us say, under the 
tremendous pressures existent at the bottom of the sea, or in 
warm springs of peculiar chemical content. In forty or fifty 
years a Berthellot or a Fischer may be producing endless varieties 
as readily as they do new chemical varieties of sugar now. 

It seemed worth while to be somewhat explicit upon the 
point in view of the extraordinary persistence of the idea that 
the chemical processes of life are any whit more mysterious 
than the chemical processes which produce salt or sugar or 
glass, or result in the burning of coal in the grate. The pre- 
ferences of the atoms, their tendency to combination — ^what in 
vague phrase we caU chemical affinity — is one of the three or 
four great world mysteries. The especial atomic association 
which displays the phenomena of life is not now a mystery 
save in the most restricted sense. It is no more of a mystery, 
let us say, than the laws of the weather. 

The parallel is perhaps very close. The weather sharp now 
knows the most, though not all, of the physical conditions which 
produce the varieties and eccentricities of atmospheric pheno- 
mena. The bio-chemist understands the most, but not all, of 
the physical conditions which result in the display of life by 
'' inert " matter. But he cannot, as yet, foUow these conditions 
sufficiently close to produce life, just as the weather-prophet 



COSMIC EXCHANGE OF MATTER AND LIFE 441 

cannot yet predict earthly weather five hundred years hence, 
as he will be able not distantly to do. Probably the solution of 
the one problem will be reached almost as soon as the other. 

But if the interesting speculation here detailed could be 
justified, we should then be in possession of a conceivable 
mechanism by which life is propagated and distributed through- 
out the universe. The implication of this will hardly escape. 
The cosmic exchange of matter means that the material of the 
universe is more or less alike. Not for the most distant planet 
of the most distant star can we conceive of any other forces 
in play than those which exist upon our earth and within our 
solar system. It follows that with the same forces, acting upon 
the same materials, the physical evolution of the suns and 
planets will be the same throughout. These are the conclusions 
to which every scrap of knowledge we possess unmistakably 
points. 

If the course of stellar and planetary evolution is the same, 
it follows that vital evolution and the forms of life will differ 
little. This we should infer from whatever point of view we 
consider its origin. If it be an incident of planetary cooling — 
that is to say, spontaneous to each cooling planet — or if it be 
propagated from one world system to another, after the manner 
so daringly imagined by Arrhenius, the result would be the 
same. 

We may go further. Intelligence — that is, our mental 
faculty — is simply a function of a definite physical organisa- 
tion. Then just as it is impossible to conceive life qualitively 
different from that upon the earth, so nowhere in the universe 
can we conceive of forms of intelligence of a different order 
than our own. The development may be higher as we know 
that it may be lower. It may envisage more facts, its deduc- 
tions may be swifter, its generalisations wider. Its limitations 
wiU remain more or less our limitations. The problems that are 
transcendent to us are, we may infer, transcendent throughout 
the universe, so far as that universe will ever be known to us. 

Such at least seems the implication of that unending process 
of give and take which we now know to be at work through- 
out the last corners of the stellar scheme. If we could travel 
for a lifetime with a thousand times the swift rush of Ught, we 
should probably fail to discover any world, any race, any in- 
telligence differing perhaps more widely from our own than 



442 THE WORLD MACHINE 

Columbus and his followers found when the new Indias were 
unveiled. A universe that is to all our human intents im- 
measurably vast is likewise immeasurably old. The universal 
effect of commerce is to obliterate differences and establish a 
relative sameness, such as now obtains throughout our human 
trading world. It cannot be otherwise with the commerce of 
the stars. The cosmic exchange, operating through immeasurable 
time, must likewise have traded the universe into a more or less 
uniform mode. 

Cosmos is wide, cosmos is old, cosmos is kin. What holds it 
together ? 



CHAPTER XXXIII 
THE LAST RIDDLE 



Ah, what a dusty answer gets the soul 
When hot for certainties in this our Hfe. 

George Meredith. 



CHAPTER XXXIII 

THE LAST RIDDLE 

There can never be in human knowledge any such thing as 
finality. Always at the end there is a mystery ; it will always 
be there. Still in a relative way we do seem here and there to 
approach something like finality. We have reached something 
like finality in the explanation of the planetary mechanism. 
So far as we are now able to perceive the planets form a system 
that, internally at least, is stable. So far as we now know, if 
they were undisturbed by any exterior agency, they would pursue 
their orbital ways for ever. It may be that subtle causes are 
at work eventually to disturb this apparent equanimity. If 
there are, they are too minute in their action to be observed. 
For all of our human concerns the sun long since will have 
been snuffed out and life upon any of the planets become im- 
possible before they would begin to have an appreciable effect. 

The dominating, binding force of the system of the planets 
we call gravitation or attraction. When we endeavour to con- 
ceive of a similar system for the stars we are lost. We can 
imagine no such binding force. Considering their speed, the 
spaces that intervene between the stars seem insuperable. The 
force of gravity, the attraction of one particle of matter for 
another, is practically the weakest force we know. It requires 
the minutest measurements of which man is capable, to disclose 
the existence of this attraction between two earthly bodies. 

Even the attracting force of such an enormous mass as the 
sun, exerted upon the huge bulk of the earth, is representable 
by very familiar strengths and strains. An ingenious com- 
parison has been made by Professor Young. He pictures the 
earth as attached to the sun by means of telegraph wires. 
Their own weight of course disregarded, it would require a 
system of wires spaced a half-inch apart, and covering the 
whole of the surface presented to the sun, to hold the earth in 
leash. When we consider that each wire would hold a section 



446 THE WORLD MACHINE 

of the earth on the average four thousand miles in length, and 
that the average density of the earth is five times that of water, 
it will be seen that this is a comparatively slight pull. 

Even within our planetary system it becomes very much less. 
Neptune is thirty times more distant from the sun ; the force 
of gravitation there is, then, nearly a thousand times slighter 
than upon the earth. A series of telegraph wires spaced forty 
feet apart would be strong enough to hold Neptune to its 
accustomed way. Consider, then, how feeble would be the 
force of gravity at the distance of the nearest star. 

It is easy enough to compute the mutual attraction of alpha 
Centauri and the sun. They are distant 277,000 times the earth 
from the sun. The force of alpha Centauri' s attraction upon the 
earth, then, is something like 75,000 million times less than that 
of the sun. The mutual attraction of our sun and the nearest 
neighbour sun, since they have apparently about the same 
mass, would only be twice this amount. It is inconceivably 
small. If we were to conceive these two suns as forming a 
binary system, the one determining the path of the other, it 
would require millions of times this attracting force to hold 
them in their orbits, with the suns moving at perhaps ten or 
fifteen miles per second. 

It does not seem possible, from any conceptions which we 
can now frame, to think of the sun as a part of a system. If 
the spacing of the stars — that is to say, the suns which we are 
able to see — be at anything like this average distance, we are 
equally lost in our endeavours to conceive of any unitary stellar 
system as well. Whence, then, the force which moves the sun, 
and gives the stars their speed ? This is the celebrated problem 
proposed by Simon Newcomb, and computed by him for a 
special instance. 

Since the days of Newton and Leibnitz, the mathematicians 
play with infinities as deftly as a Japanese juggler with plates 
and sharp knives. It is not difiicult for a mathematician to 
reckon up what speed a body might attain in falling from infinity 
towards a known mass with a known attractive force. The 
case for the stars is stated thuswise by Professor Newcomb : 

The telescope discloses something more than fifty million 
suns ; suppose that we double this number, and give to each of 
these suns five times the mass of our own. In other words, 
let us conceive of a stellar universe equivalent in its mass to 



THE LAST RIDDLE 447 

five hundred million suns like ours. The telescopes reveal the 
existence of stars distant possibly thirty thousand light-years 
or more. Let us conceive this mass distributed over an equivalent 
extent of space. Conceive that a star is drawn from an infinite 
distance towards the centre of this system : what is the utmost 
speed which it may acquire ? The very surprising answer is 
twenty-five miles per second. 

But we have seen that Arcturus and 1830 Groombridge move 
at two or three hundred miles per second. Of course if one sun 
approached very close to another, the case would be quite 
different. For example, a body approaching the sun may 
acquire a velocity of nearly four hundred miles per second. For 
such a mass as that of Arcturus, still more of Canopus, this 
velocity would be very much greater. It may be that it is 
from their occasional approach one to another that the stars 
acquire some of the speeds that they are known to possess. 
This would obviate one difficulty ; but not its correlative. 

If such a steUar universe as Professor Newcomb imagines is 
incapable of generating a velocity like unto that of Arcturus or 
Groombridge, it is obvious that it could not hold a star or sun 
with such a speed in leash. If Arcturus is moving at three 
hundred miles or more per second, it would require a mass one 
hundred and forty-four times that of five hundred millions suns 
to keep this speeding sun from dashing away into the depths 
of space. If our stellar system were finite, and of less mass 
than this, Arcturus would be lost to it. 

Arcturus is but probably one case in many. There may be 
hundreds and thousands of suns, for aught we know, moving 
very much more rapidly than this. If ever the stars formed a 
relatively compact system, they might, in this view, have been 
steadily losing one sun after another. In so doing the system 
would be steadily losing mass, with the result that it would 
progressively lose whatever power it may originally have pos- 
sessed to hold together. 

Of course all this is merely the vaguest conjecture. We 
know absolutely nothing about the mass of the universe save 
perchance one thing. Seeliger of Munich has pointed out that 
the idea of an infinite universe is incompatible with the notion 
that the law of gravity is absolute and invariable. Seeliger 
assumes that the law is not absolute, and that the force of 
gravitation does not increase or decrease in perfect conformity 



448 THE WORLD MACHINE 

to the law of inverse squares.^ It may be remarked that such 
an assumption is required by the electro-dynamical theory of 
gravitation ; but there is not the slightest evidence as yet that 
such a diminution takes place. If it does not, it would follow 
of course from an infinite universe that we should have stars 
and other bodies moving at infinite speeds. 

We are undoubtedly obliged to make option between the two 
possibilities, and to the writer it has always seemed that the idea 
of a finite universe was preferable. Of course, either finite or 
infinite is in reality unthinkable ; we can conceive the one as 
little as the other. But since the human mind is so constituted 
that it can frame no working conceptions of the universe which 
are not mechanical conceptions, it is a part of the economy of 
thought to believe that, for all our means of observation will 
ever tell us, the mass and number of the stars is a finite quantity. 

If it be finite, it is possible that some other force, or forces, 
exist to determine stellar motions than those of gravitation. 
But the necessity for any such assumption may be dissipated 
with the increase of our knowledge. There is distinctly such 
a possibility in the probable number of dark bodies. Their 
number and mass might be sufiicient to produce any stellar 
speeds with which we are at present acquainted. 

Even conceding this, if gravitation be the only effectual 
inter-stellar force, we should probably have to give up the 
notion that there exists any stable arrangement of stellar 
systems. We should probably have to picture the starry 
scheme as we have done, in something after the same fashion 
as the kinetic theory of gases. The stars would simply be 
flying in every direction without any conceivable order whatever. 

This is a part of the riddle. There still remains the larger 
one of the nature of gravitation itself. 

When Newton revealed the presence of an attracting force 
between aU masses of matter, it was objected by his contem- 
poraries that such a force was unthinkable. It remains so still. 
Newton's theory (not Newton himself) conceived space as to all 
intents and purposes empty. But so constituted is the human 
mind that while we may picture — that is to say, understand — one 
body imparting motion to another by impact, we cannot picture 
an attraction or pull without an intervening medium. 
1 Sitzungsberichte d. Munchener Akad., 1896. 



THE LAST RIDDLE 



449 



This was a great stumbling-block to the acceptance of the 
new gravitation theory. It involved the idea of action at a 
distance. This is one of the inconceivables. No one saw this 
more clearly than Newton himself. He had a highly speculative 
mind — that is to say, a very vivid imagination, scientifically 
trained. He tried to think out a method by which this ap- 
parent attraction could be accounted for. No abler head ever 
pondered the subject. It is of interest to know precisely 3,how 
he conceived the problem. 

To the end of his days Newton refused to consider gravitation 
as an inherent property of matter. So far as his physical specu- 
lations were concerned, he was a thorough materialist. But as 
late as 1717, in the second edition of his Opticks he wrote : — 

" At the end of the Third Book I have added some Questions. 
And to shew that I do not take Gravity for an essential Property 
of Bodies, I have added one Question concerning its Cause, 
chusing to propose it by way of a Question, because I am not 
yet satisfied about it for want of Experiments." 

This same thought pervades the Principia. At the very 
beginning of the work, as his eighth Definition, he says : — 

" Wherefore the reader is not to imagine that by these words 
I anywhere take upon me to define the kind or the manner of 
any action, the causes or the physical reason thereof, or that I 
attribute forces, in a true and physical sense, to certain centres 
(which are only mathematical points) when at any time I happen 
to speak of centres as attracting or as endued with attractive 
powers." 

As Newton was the first to grasp the idea of attraction, so 
was he the first to speculate upon its cause. At the end of 
the Principia we find this pregnant paragraph : — 

*' Hitherto we have explained the phaenomena of the heavens 
and of our sea by the powers of gravity, but have not yet assigned 
the cause of this power. This is certain, that it must proceed 
from a cause that penetrates to the very centres of the sun and 
the planets, without suffering the least diminution of its force ; 
that operates not according to the quantity of the surfaces of 
the particles upon which it acts (as mechanical causes used to 
do) but according to the quantity of the solid matter which 
they contain, and propagates its virtue on all sides to immense 
distances, decreasing always in the duplicate proportion of the 
distances. Gravitation towards the sun is made up out of the 

2 F 



450 THE WORLD MACHINE 

gravitations towards the several particles of which the body of 
the sun is composed ; and in receding from the sun decreases 
accurately in the duplicate proportion of the distances as far as 
the orb of Saturn, as evidently appears from the quiescence of 
the aphelions of the planets ; nay, and even to the remotest 
aphelions of the comets, if those aphelions are also quiescent. 
But hitherto I have not been able to discover the cause of those 
properties of gravity from phaenomena, and I frame no hypo- 
theses [hypotheses non fingo) ; for whatever is not deduced from 
the phsenomena is to be called a hypothesis ; and h37potheses, 
whether metaphysical or physical, whether of occult qualities 
or mechanical, have no place in experimental philosophy. In this 
philosophy, particular propositions are inferred from the phaeno- 
mena and afterwards rendered general by induction. Thus it 
was that the impenetrability, the mobility and the impulsive 
force of bodies, and the laws of motion and of gravity were 
discovered. And to us it is enough that gravity does really 
exist, and act according to the laws which we have explained, 
and abundantly serves to account for all the motions of the 
celestial bodies and of our sea." 

In a celebrated letter to Sir Robert Boyle on this subject, 
Newton gave freer range to his imaginative faculties, and 
endeavoured to show how the phenomena of gravitation might 
flow from the supposition of a very tenuous " aether "—something 
of the same sort of concept as physicists have since imagined 
to explain the phenomena of light. It is of interest as affording 
a glimpse at the workings of a great mind, as do the letters of 
Faraday and Darwin. Let the grubbing brain that never lifts 
its eyes into the speculative blue above, consider this curious 
passage : — 

** I will suppose aether to consist of parts differing from one 
another in subtilty by infinite degrees ... in such manner that 
from the top of the air to the surface of the earth, and again 
from the surface of the earth to the centre thereof, the aether 
is insensibly finer and finer. Imagine now any body suspended 
in the air or lying on the earth, and the aether being by the 
h5^othesis grosser in the pores which are in the upper parts of 
the body than in those which are in the lower parts, and that 
grosser aether being less apt to be lodged in those pores than 
the finer aether below, it will endeavour to get out and give way 



THE LAST RIDDLE 451 

to the finer aether below, which cannot be without the bodies 
descending to make room above for it to go into." 

In the 2ist of his celebrated queries, in the Opticks, Newton 
elaborates his ideas still further, endeavouring even to con- 
ceive what the properties of the cither must be in order that 
it might serve as an explanation of this inexplicable power. It 
runs : — 

" Is not this Medium much rarer within the dense Bodies of 
the Sun, Stars, Planets, and Comets, than in the empty celestial 
spaces between them ? And in passing from them to great 
distances, doth it not grow denser and denser perpetually, and 
therefore cause the gravity of those great Bodies towards one 
another, and of their parts towards the Bodies ; every Body 
endeavouring to go from the denser parts of the Medium towards 
the rarer ? For if this Medium be rarer within the Sun's Body 
than at its Surface, and rarer there than at the hundredth part 
of an Inch from its Body, and rarer there than at the fiftieth 
part of an Inch from its Body, and rarer there than at the Orb of 
Saturn ; I see no reason why the Increase of density should 
stop anywhere, and not rather be continued through all dis- 
tances from the Sun to Sahirn, and beyond. And though this 
Increase of density may at great distances be exceeding slow, 
yet if the elastick force of this Medium be exceeding great, it may 
suffice to impel Bodies from the denser parts of the Medium 
towards the rarer, with all that power which we call Gravity. 
And that the elastick force of this Medium is exceeding great, 
may be gathered from the swiftness of its Vibrations. Sounds 
move about 1140 English Feet in a second Minute of Time, and 
in seven or eight Minutes of Time they move about one hundred 
English Miles, Light moves from the Sun to us in about seven 
or eight Minutes of Time, which distance is about 70,000,000 
English Miles, supposing the horizontal Parallax of the Sun to 
be about 12''. And the Vibrations or Pulses of this Medium, 
that they may cause the alternate Fits of easy Transmission 
and easy Reflexion, must be swifter than Light, and by con- 
sequence above 700,000 times swifter than Sounds. And there- 
fore the elastick force of this Medium, in proportion to its 
density, must be above 700,000 x 700,000 (that is, above 
490,000,000,000) times greater than the elastick force of the 
Air is in proportion to its density. For the Velocities of the 
Pulses of elastick Mediums are in subduplicate Ratio of the 



452 THE WORLD MACHINE 

Elasticities and the Rarities of the Mediums taken to- 
gether." 

When some of Newton's followers proposed flatly to accept 
actio in distans Newton would have nothing whatever to do 
with it. In his well-known letter to Bentley he evidences his 
impatience. He says : — 

" It is inconceivable that inanimate brute matter can, without 
the mediation of something else which is not material, operate 
upon and affect other matter, without mutual contact, as it 
must do if gravitation, in the sense of Epicurus, be essential and 
inherent to it. This is the reason why I desire that you would 
not ascribe an innate gravity to me. That gravity should be 
innate, inherent, and essential to matter, so that one body may 
act upon another at a distance, through a vacuum, without the 
mediation of anything else by and through which their action 
may be conveyed from one to another is to me so great an 
absurdity that I believe no man, who has in philosophical matters 
competent faculty of thinking, can ever faU into. Gravity must 
be caused by an agent acting constantly according to certain 
laws ; but whether this agent be material or immaterial, I 
have left to the consideration of my readers." 

The riddle of Newton's time remains a riddle to our own. 
In some regards the mystery has deepened rather than cleared. 
One of the greatest works of the last century was undoubtedly 
the establishment of the idea of the conservation of energy ; 
but gravitation is a standing negation of such a concept. So 
far as we can see now, it represents an inexhaustible supply of 
energy with no corresponding dissipation. It is true that so 
far as our earthly concerns go we are not able to utilise gravita- 
tion for the estabhshment of perpetual motion ; but possibly 
the universe does. According to our present ideas it is the im- 
pact of suns,^ doubtless for the most part cold suns, combined 
with the heat of attraction, which gives rise to the incandescence 
of the stars. When this initial store of energy has been dis- 
sipated and the suns become cold again, they have merely to 
come into a second collision that the cycle may be resumed. 
So far as we can now see this might go on for ever. The 
universe itself might realise that perpetuity of utilisable force 
or energy which is denied to man. 

^ James CroU, Stellar Evolution. 



THE LAST RIDDLE 453 

This is part of the puzzle. Another is the apparently in- 
stantaneous propagation of gravitation. Attraction is a force, 
and every other force with which we are acquainted requires a 
finite time for its extension through space. Endless endeavours 
have been made to discover a rate of propagation. Laplace was 
among the many who tried it. He thought for a time that 
he had ; latterly he gave it up. Very recently a German 
mathematician, Gerber, thought to deduce the rate from the 
motion of perihelion of Mercury. i This is estimated at forty- one 
seconds in a century, and according to Gerber' s computations 
this would indicate a rate of propagation for gravitation similar 
to that of light and electric waves. It remains as yet merely 
a plausible theory. 

A further mystery of gravitation is that it cannot be screened. 
It acts apparently with the same force through a planet as through 
empty space. When the planetary bodies are in conjunction — 
that is to say, in a straight Hne from the sun one with the other — 
they swerve slightly perforce of their own mutual attractions; 
but not otherwise. It needs be said that in this regard gravita- 
tion does not stand absolutely alone. The same thing is true 
of magnetism. We are equally unable to devise a magnetic 
screen. If we could do either we should have perpetual motion, 
and, more than this, we should be able to navigate space. 

It is obvious that so long as we know nothing of the theory 
or ** cause" of the most famihar fact of our daily lives, we 
cannot advance very far. Countless efforts have been made to 
break through this impasse ; none have succeeded — that is, 
if we bar the philosophers. Readers with a taste for such 
things will doubtless find interest in a recent volume of Pro- 
fessor Wilhelm Ostwald,^ wherein the difficulties which have 
beset a considerable line of hard-headed thinkers, from Newton 
to Kelvin, are lightly brushed away. 

In a scientific sense, probably the most noteworthy attempt 
towards an explanation was the hypothesis proposed by Lesage, 
a modest physicist of Geneva, about a hundred and fifty years 
ago. Lesage, who is in no wise to be confounded with the 
author of Gil Bias, suggested that the facts of§ gravitation 
might be accounted for by conceiving of an infinite rain or 
hail of infinitesimal particles, driving about in every direction 

1 Zeitschr. f. Math. u. Phys. 1898, II. 
2 Vorlesungen uher N aturphilosophie ; Leipzig, 1902, p. 193. 



454 THE WORLD MACHINE 

with an average equal motion, and so small that they would 
penetrate and flow through all forms of matter whatsoever. 
Because this rain must be incessant and to all intents infinite, 
Lesage conceived it to come from beyond the confines of the 
known universe ; hence he called these flying bodies ultra- 
mundane particles. 

It will be perceived that Lesage's idea of an eternal downpour 
of minute particles of matter does not differ very greatly from 
the ideas of Democritus and Epicurus. It is evident from his 
memoir that it was a reading of these which probably suggested 
the hypothesis he framed. It was, to be sure, a purely specu- 
lative conception. It was a kind of an explanation ad hoc. 
Before us is a fact — how might it be explained ? We have of 
course not the.° slightest evidence that any such corpuscular 
downpour takes place. 

Still, it is noteworthy that Lesage's hypothesis has been 
favourably entertained by more than one acute and penetrating 
mind, in especial, that of S. Tolver Preston, an English physical 
philosopher who gave high promise ere he died. It was Tolver 
Preston who pointed out that the scheme imagined by Lesage 
differed but little from our present-day theory of gases, of the 
cause of the pressure of air, &c. His postulates were much the 
same.^ We should merely have to imagine an order of cor- 
puscles as much smaller let us say, than the molecules or 
particles of air as the latter are smaller than small shot or sand. 

Very recently in the emanations of radium we have learned 
to know of a corpuscular order perhaps a thousand times smaller 
than the smallest of the atoms, possibly hundreds of thousands 
of times smaller than the molecular aggregations of air or vapour. 
There is nothing a priori to forbid our imagining that a' yet more 
minute order exists, and sufficient in numbers to satisfy the 
assumptions of Lesage as they were modified in the mind of 
Preston. Probably we are as yet merely upon the rim of physical 
knowledge. Of what another two or three centuries like the 
last may bring forth we have of course not the remotest sus- 
picion. But so far as our present-day knowledge extends, the 
theory is little more than a brilHant fancy. 

Endeavours at an explanation of a hydro-dynamical sort have 
not been few. It has been known for a very long time that 
pulsating spheres, immersed in an incompressible medium Uke 
1 Philosophical Magazine, 1878-79. 



THE LAST RIDDLE 455 

water, attract each other and tend to approach. In the sup- 
position of a Hght-bearing ether we have something of such an 
incompressible medium, supra-sensible to our present methods 
of observation ; if we could conceive of every ultimate particle 
of matter as a pulsating sphere, then we might have here an 
explanation of attraction. But it was pointed out by Arago, 
and doubtless by many another before him, that such pulsa- 
tions would require a definite time for their propagation. The 
theory stumbles over the fact that no finite speed for gravitation 
can be detected. 

This order of ideas has recently found an ingenious extension 
at the hands of two Swedish investigators, C. A. and Victor 
Bjerknes, father and son. Their work has given emphasis to 
the idea that it is to such a hypothetical ether that we must 
look for the ultimate explanation of the interaction of all forces. 
By means of such an assumption we may do away with the 
utterly unthinkable notion of action at a distance ; but it must 
be said that the various attributes framed for this highly useful 
ethereal medium are as absolutely incongruous as the incon- 
gruous conceptions it is designed to avoid. There never was 
folly more sheer than to suppose that we can think of con- 
tinuous extended substance in which matter or material bodies 
may move. Perhaps this is no worse than our endeavours to 
conceive of an atom which cannot be divided. We have here 
passed the limit of experimental proof and stepped into a realm 
where we are offered the choice of fancy or metaphysics. The 
one is undoubtedly of as much value as the other, with the 
difference perhaps that where ingenious fancy has sometimes, 
if rarely, pointed to new paths of discovery, metaphysic has 
never. It is a fatal anodyne to physical inquiry, the relaxation, 
sometimes, in summer moods, for healthy minds ; their staple 
diet never. It is the predilection, the writer has long been 
convinced, only of cobweb brains, lost in the phantasies of a 
mild distemper. 

In such a summer mood, amid serene days when the mind 
refuses to be vexed with difficulties, even the most obvious and 
insuperable, let us turn the last page. Above me, as I look high 
over the hills, the azure is entrancing in its beauty, boundless, 
so far as I can ever know. For the spacious abstraction we call 
the universe we can imagine no end ; its annihilation is unthink- 



456 THE WORLD MACHINE 

able. Yet the irresistible bent of the mind which leads me to 
believe that I am I, and to lend to the exterior world an objective 
existence, illusory though it may be, determines that I shall 
also recognise in the concourse of phenomena a definitive 
tendency or direction. A machine that can go on for ever is 
no machine. The energy of the universe may be constant ; 
but that part of it which is utilisable apparently tends to lower 
and lower levels ; in a Clausian sense, the sum of entropy is 
increasing. This, in scholastic phrase, can only predicate final 
immobility. If, as all our reason peremptorily demands we 
believe, we are part and cog of a cosmic mechanism, we must 
look to its fate. 
What will it be ? 



CHAPTER XXXIV 
THE END OF THE MACHINE 



Now sit we close about the taper here, 
And call in question our necessities. 

Julius CcBsar, iv. 3. 

But, Socrates, the sun I think is still upon the mountains, and 
has' not yet gone down. 

Plato, Crito. 



CHAPTER XXXIV 

THE END OF THE MACHINE 

An impenetrable veil hides from us the beginning of things. So 
far as we can now see, it will never be lifted. Equally from 
our view is veiled the end. The forces with which physical 
investigations deal are finite ; they are measurable, and, in a 
way, simple. The single exception to this — and that may be 
only an apparent exception, the outcome of our present ignorance 
— is gravitation. So long as that riddle is unexplained, it is 
idle to conjecture. Perhaps it would still be idle if it were 
solved. 

So far as we can now perceive there appears to be, in Spen- 
cerian formula, an increasing aggregation of matter. If the 
matter of the universe is finite, and if this aggregation be pur- 
sued indefinitely, it could have but one result : that would be 
final congregation into a single mass. The universe of suns 
and planets would be tumbled into a single lump. 

Whatever be the larger fact, it is not improbable that this 
may be the fate of that part of cosmos which it will ever be 
given to our human kind to know. There is much in recent 
stellar discovery to suggest such a conclusion. It is obvious, 
for example, that, if we do not mistake as to the vast size of 
Canopus, we should have here a relatively advanced stage of 
the process. 

If the meteoritic idea of the origin of suns and planets hold 
aught of truth, the tendency is towards the formation of larger 
and larger bodies. Each of these would act in some sense as 
centres of aggregation. It is fairly clear that in the course of 
ages the earth has grown, all of the planets have grown, the 
sun itself has grown. The continuous sweeping of these 
large bodies would eventually empty space of all its minor 
contents. 

If we prolong our vision we shall see that amid the alternate 
formation of systems, and their disintegration through stellar 



46o THE WORLD MACHINE 

collisions, there would yet be a tendency towards the accumula- 
tion of matter into ever narrower areas. Presently this would 
produce one enormous body which no collision would shatter. 

It is obvious, for example, that the collision of our sun and 
Canopus would not mean a dissipation. If the earth fell into 
the sun, even at enormous speed, its mass is yet too slight to 
cause the dissipation of the mass of the sun into primeval 
nebula. In the light of our present estimates, precisely the 
same thing would be true if our sun were drawn into Canopus. 
It would add something to the heat of that star ; it would add 
something to its mass. Canopus would not be destroyed. 

We know nothing of the motion of Canopus. If it were 
careering through space at the speed of Arcturus, it would be 
sweeping up suns at a relatively tremendous rate. Whether it 
be in motion or no, the result would be much the same. We 
might even conceive it as standing still, and since we know that 
the stars about it are moving rapidly in every direction, in 
the end they would one by one approach and be drawn within 
its gigantic spider's web. 

We might, of course, conceive that a similar process was at 
work throughout other regions, with the resultant formation of 
other suns equal in grandeur to Canopus. If two such suns in 
their turn came in collision, the result would probably mean the 
dissipation of both into a primitive nebulous condition. But 
there would be this difference, that whereas the matter of which 
they were composed had originally extended over vast areais, 
that which would be occupied by the new nebula thus formed 
would probably cover but a small extent of the former. If 
contraction then took place, the resultant system would ap- 
parently have one vast sun at its centre instead of the original 
pair. The process which had been followed out by each of them 
would, after the elapse of an immense period of time, be resumed 
with double the energy — that is to say, with double the attracting 
force. 

So far as we can now see, there is little to stay and nothing 
to limit such a process. The end might be delayed through 
aeons of time, compared with which the life-history of our solar 
system would appear but seconds in a seeming eternity. It 
could have but the result which we have surmised. This central 
mass would dissipate its heat, it would cool just as our planet 
has cooled, just as the sun is cooling, just as great Canopus 



THE END OF THE MACHINE 461 

will cool. If there were planets revolving about it, a time 
would come when life upon them would be impossible. The 
image of the universe then would be that of an inert clod, 
mindless, helpless, motionless, and dumb. 

All this, it scarce needs saying, is but the purest speculation. 
Arrhenius, for example, has quite another view, offering, in his 
textbook of cosmical physics, the idea that the matter of the 
universe follows a continual round of alternating aggregation 
and dispersion. The penetrating mind of this great Swedish 
investigator conceives that this knows no end. In a private 
note to the writer he very trenchantly observes : — 

*' Formerly we knew only of the Newtonian force of gravita- 
tion, and therefore cherished the idea that in the end everything 
would clump together. But we now know of the pressure of 
radiation which may balance the tendency of congregation. At 
the catastrophe of Nova Persei it was observed that hydrogen 
shot out from the star with a velocity of about 700 kilometres 
per second. If Nova Persei is of the same magnitude as our 
sun, this velocity is so great that it would drive the hydrogen 
out from the gravitational field of the star into infinite space. 
Many nebulae — e.g. that of the Pleiades or Orion — indicate by 
their extraordinary dimensions such a diffusion into practically 
infinite distances. 

'* I therefore adhere to the idea of an oscillation of matter 
because it is impossible for me to understand a beginning or an 
end of the system of matter that we observe. If there were an 
end, with complete rest, the condition would have been reached 
in the infinity of time which lies behind us, and there would be 
nothing left in the world for us to observe. Therefore also the 
second law of thermo-dynamics cannot be perfectly true as it is 
formulated now." 

The justice of these observations is evident. Yet it is difficult 
to understand how the balance could be maintained simply from 
the pressure of radiation without assumptions which as yet 
have but a slight foundation. We might conceive, of course, 
that the heat generated by the contraction of a nebulous mass 
increases with the mass, and we might therefore imagine that 
bodies enormously larger than our sun are likewise enormously 
hotter. There is Uttle, however, as yet, to suggest that such 
is the case. The conclusions of Sir William Huggins, in fact, 
are directly the contrary. He supposes that the maximum of 



462 THE WORLD MACHINE 

temperature is reached in bodies at the evolutionary stage of 
our own sun. If this were true, the pressure of radiation from a 
body of the conjectural dimensions of Canopus would be quite 
insufficient to counterbalance its gravitational pull. The process 
of aggregation might be delayed, but in the unthinkable reaches 
of time which we are considering it would still be consummated. 
The very acute observation that if any such process were 
at work it would have been completed long ago, lays bare 
the real dilemma. It is evident enough that the problem is 
in reality transcendent. 

Such gigantesque if somewhat tenuous speculations mark in 
some sense the highest attainments of the human mind. Re- 
flecting upon its lowly origin — considering its stumbling, groping 
beginnings — comprehending in a single sweep the tremendous 
range of its activities — ^we shall not err, perhaps, if we consider 
that the true world-marvel is the mind itself. Reluctantly, 
and with the painful sense as of a hobble cast about the feet of 
some splendid courser, every fibre of his body trembling with the 
excitement of the chase, we recurrently awake to the realisation 
of its finite limitations. 

From such heights we must descend at intervals to consider 
the rather slender foundations upon which it rests. It was 
Hume who pointed out that all we know of cause is reiterated 
sequence, the constant succession of events. It is this constant 
succession which we call law. It is upon this which rests the 
vast body of co-ordinated knowledge which we may regard as 
in some sense permanent, an inexpugnable fortress. It is with 
the aid of these same materials that speculatively we hft our 
kites and aeroplanes to tour the blue above. 

But it is evident that we can have no idea as to the past, 
no surmise as to the future, save that which is based upon the 
supposition that this constant succession is never changed. 
Moreover, the facts which we have to go on are as yet slight. 
The law of gravitation is hardly more than two hundred years 
old. The idea of conservation of energy dates back little more 
than half a century, a couple of generations. It is only within 
forty or fifty years that man has had any reasonable basis upon 
which to speculate as to his origin or his future. 

This fact bids us exercise a certain, if indulgent, scepticism 
towards any very rigid conclusions. We need not cast aside 



THE END OF THE MACHINE 463 

sense or science. We need not throw ourselves into the in- 
tellectual muck of astrology, spiritism, or degrading gullibility. 
But we may remember that time is long. To set out the matter 
well, Professor Langley has drawn the threads of his fancy into 
a graceful parable, whose import will ever be salutary : — 

" We have read somewhere of a race of ephemeral insects who 
live but an hour. To those who are born in the early morning, 
the sunrise is the time of youth. They die of old age while its 
beams are yet gathering force, and only their descendants live 
on to mid-day ; while it is another race which sees the sun's 
decline from that which saw it rise. Imagine the sun about to 
set, and the whole nation of mites gathered under the shadow 
of some mushroom (to them ancient as the sun itself) to hear 
what their wisest philosopher had to say of the gloomy prospect. 
If I remember aright, he first told them that, incredible as it 
might seem, there was not only a time in the world's youth 
when the mushroom itself was young, but that the sun in those 
early ages was in the eastern, not the western, sky. Since 
then, he explained, the eyes of scientific ephemera had followed 
it, and established by induction from vast experience the great 
* Law of Nature ' that it moved only westward ; and he showed 
that since it was now nearing the western horizon, science her- 
self pointed to the conclusion that it was about to disappear 
for ever, together with the great race of ephemera for whom 
it was created. What his hearers thought of this discussion I 
do not remember, but I have heard that the sun rose again the 
next morning." ^ 

This is excellent. Yet the codified experience of the human 
race is of worth. Reason, inference, induction, synthesis, will 
ever remain the only means of dispelling the environing ignorance 
into which we are born, or of effecting any amelioration of our 
human lot. For the here and now it is our sole guide. So far 
as it may surely lead, wide-eyed and fearless, we must follow. 

For the rest it is not probable that the main results of the 
last two or three centuries will ever be materially impaired. 
Our ideas and our presentation of them will insensibly change. 
The facts undoubtedly will remain. What we have to consider 
is that perhaps a very slight modification of our present ideas 

1 Langley, The New Astronomy. 



464 THE WORLD MACHINE 

might suffice greatly to change our ideas of the future. The 
discovery of radium and the cathode radiations, emanations, of 
the pressure of radiation, and the Hke, to all of which reference 
has repeatedly been made, may very distinctly alter our ideas as 
to the age of the earth, of the sun as well. In the course of 
three or four centuries, three or four other discoveries may 
come of yet more vital import. ; 

There is, however, one central fact which, for aught we may 
now see, may never be modified and from which we can never 
escape. The cosmic machine runs on. We die. La vie est breve, 
la vie est court. It seems fairly incontestable that life had a 
beginning upon the earth, and, what is of much deeper import, 
there was a time in the history of the earth when it bore no 
human race. So far as we can see, that which has a beginning 
must also have an end. When the candle of the sun has been 
burnt to its socket, the cycle of evolution which produced our 
race wiU have turned downwards and backwards, returning to 
the bathybii and lichens from which we sprang. 

The history of the earth does not suggest a high importance 
for the individual human life. We may roughly estimate the 
period of man at from two to five hundred thousand years, 
perchance a million — let us say, roughly, ten to thirty thousand 
generations. It does not seem probable that the number of 
human beings on earth has varied very greatly in ten or twenty 
thousand years, perhaps not in fifty thousand. At present the 
number is about fifteen hundred millions — in American notation, 
a billion and a half. The personnel of this number is changed 
on the average once in twenty-five or thirty years. 

It is easy to see that the aggregate number of human beings 
who have ever lived upon earth runs into hundreds, it may 
be thousands, of billions. The lives of the vast majority of these 
were of as much consequence to human history as the spawn of 
fishes or the larvae of flies. It is considerations of this sort which 
make it difficult to understand at times the ardour with which 
men pursue the shows and baubles of this world. 

The individual life is of little consequence to the race. The 
aggregate life of the race seems of little consequence to the 
earth. BilHons upon billions of coral polyps may materially alter 
the surface of the globe. Probably their work will be of more 
consequence, will have effected greater changes in terrestrial 
conditions, than all that will ever be effected by man himself. 



THE END OF THE MACHINE 465 

It may be that the human race has yet a long time to run, 
compared with the relative brevity of its past. It may be that 
human achievement has hardly begun. Be that as it may, it 
will one day be finished. 

So far as we can now perceive, human civilisation is but a 
flutter of consciousness amid the wide cycle of life that sweeps 
through from hchen and bacterium to saurian monster and 
back again. And the cycle of life is but an evanescent moment 
in the history of the globe. The history of the globe is in its 
turn but an evanescent moment in the cycle of the stars ; suns 
glow for a little time, and planets bear their fruitage of plants 
and animals and men, then turn for aeons in a drear and icy 
lifelessness. We may change the moving lines of the poet 
slightly :— 

" The earth hath bubbles as the water has. 
And life is of them." 



Such is the cosmic order so far as the Book of Revelation is 
complete. That revelation has dissipated our childish dreams, 
it has shattered our childish faiths. So far as the outer world 
is intelHgible to us, the immediate portion in which we live our 
lives is simply a machine, so orderly and compact, so simple in 
construction, that we may reckon its past and gauge something 
of its future with almost as much certitude as that of a dynamo 
or a water-wheel. In its motions there is no uncertainty, no 
mystery, save the eternal mystery which will for ever shroud the 
underlying reality. This is the first fact which modern science 
has to offer to the philosophic mind. 

Accepting cosmos as a machine, dominated by simple 
mechanical laws, we still pursue our lives as if human destiny 
were the subject of human control. We may accept the 
mechanical necessity of day and night, the change of the seasons, 
the variations of climate throughout long periods. They are 
the inevitable results of the planetary mechanism. To this 
much of the idea of mechanism we are accustomed, and in- 
sensibly reconciled. 

But the wind bloweth where it hsteth, the rains cometh, 
tribes and kingdoms rise and fall. The perception of order in 
these more intimate phenomena is as yet incomplete. In a 
volume to follow, I purpose to review the advance of our insight 

2 G 



466 THE WORLD MACHINE 

into the terrestrial, the human, the social, and the economic 
mechanism, and to inquire whether in the sculpturing of the 
earth, in the course of the winds, in the fall of the rain, in the 
rise of kingdoms, in the appearance of great minds, great ideas 
or great discoveries, in the alternation of years of drouth and 
years of plenty, in dress or customs, or in the little happenings 
of our daily lives, there is any different order at work than 
that which we may observe in the cosmos at large. 



London, June 1903 ; 
Berkeley, California, April 1906. 



BENEDICITE. 

LA PAIX DES DIEUX 

Et rhomme dit : Demon ! qui hantes mes t6n6bres 
Mes reves, mes regrets, mes terreurs, mes remords ; 
O spectre ! emporte-moi sur tes ailes fun^bres 
Hors de ce monde, loin des vivants et des morts. 

Loin^des globes flottant dans I'Etendue immense 
Ou le torrent sans fin des soleils furieiix 
Roule ses tourbillons de flamme et de demence, 
Demon ! emporte-moi jusqu'au Charnier des Dieux. 

Oh, loin, loin de la Vie aveugle ou 1' esprit sombre 
Avec I'amas des jours sterile et des nuits, 
Ouvre-moi la cite du silence et de 1' ombre, 
Le sepulcre muet des Dieux evanouis. 

O d6mon ! M^ne-moi d'abimes en abimes 
Vers ces Proscrits en proie aux si^cles oublieux. 
Qui se sont tus, scellant sur leurs l^vres sublimes 
Le Mot qui fait jailler TUnivers dans les cieux. 



Alors le Compagnon vigilant sur ses reves 

Lui dit : Reste, insense ! Tu plongerait en vain 

Au celeste ocean qui n'a ni fonds ni graves. 

C'est dans ton propre coeur qu'est le Charnier divin. 

La sont tous les Dieux morts, anciens songes de FHomme, 
Qu'il a con^us, crees, adores, et maudits, 
Evoques tour k tour par ta voix qui les nomme 
Avec leur vieux enfers et leur vieux paradis. 

Contemple-les au fond de ce coeur qui s'ignore, 
Chaud de mille desirs, glace par mille hivers, 
Ou dans I'ombre eternelle et Teternelle aurore, 
Fermente, eclate et meurt I'illusoire univers. 

Leconte de Lisle, Dernihes Poemes. 



467 



BIBLIOGRAPHY 

Aside from the especial citations in the text, the materials for 
the present volume have mainly been drawn from the following 
works : — 

Cicero, Academics ; Nature of the Gods, ed. Bohn. 

Diogenes Laertius, Lives, ed. Bohn. 

(Euvres de Lucr^ce, Trad. Lagrange. 

Martha, Le Po^me de Lucrece, 1 896. 

Apelt, Die Epochen der Geschichte des Menschheit, 1845. 

Bailly, Histoire de 1' Astronomic Ancienne et Moderne, 4 vols., 1779, 
et seq. 

Delambre, Histoire de T Astronomic Ancienne et Moderne, 6 vols., 
1815, et seq. 

Whewell, History of the Inductive Sciences, 3 vols., 1847. 

Montucla, Histoire des Mathematiques, 4 vols., 1758, et seq. 

Libri, Histoire des Sciences Mathematiques, 3 vols., 1838. 

Humboldt, Cosmos, 7 vols., 1845, ^^ ^^5'- 

Lange, Geschichte der MateriaHsmus, 3 vols., 1873. 

Buckle, History of CiviHsation in England, 2 vols., 1859^ 

Lecky, History of the Rise and Influence of the Spirit of Ration- 
alism in Europe, 2 vols., 1865. 

Draper, History of the Intellectual Development of Europe, 2 vols., 
1861. 

Merz, History of European Thought, 2 vols., 1900. 

Schiaparelli, I Precursori di Copernico neU'Antichita, 1873. 

Matter, Histoire de I'Ecole d'Alexandrie, 3 vols., 1843. 

Berti, Copernico, 1876; Bruno, 1889. 

Martin, Galilee, 1868. 

Brewster, Memoirs of the Life of Newton, 2 vols., i860. 

Voltaire, Lettres Phil, sur les Anglais, 1734 ; Elements de la Phil, 
de Newton, 1745. 

Rosenberger, Newton und Seine Physikalischen Principien, 1893. 

Lewes, Aristotle, 1864. 

Galileo, Opere Complete, 17 vols., 1855. 

Descartes, (Euvres Completes, 11 vols., 1824. 

Bertrand, Les Fondateurs de 1' Astronomic, 1889. 

Berthelot, La Revolution Chimique, 1 890. 

469 



470 BIBLIOGRAPHY 

Mach, Die Mechanik in ihrer Entwickelung, 1883. Die Principien 

der Warmelehre, 1900. 
Duhem, L' Evolution des Theories Physiques, 1896. 
Lodge, Pioneers of Science, 1893. 
Berry, History of Astronomy, 1892. 
WilUams, A History of Science, 1904. 
Gierke, History of Astronomy in the Nineteenth Century, 1902. 

System of the Stars, 1905. Problems in Astrophysics, 1903. 
Wolf, Les Hypotheses Cosmogoniques, 1886. 
Helmholtz, Vortrage und Reden, 2 vols., 1903. 
Kelvin, Lectures and Addresses, 3 vols., 1889. 
CroU, Stellar Evolution, 1889. 
Tait, Recent Advances in Physical Science, 1885. 
Ball, The Story of the Earth, 1904. 
Arrhenius, Lehrbuch der Kosmischen Physik, 1903. 
Newcomb, Popular Astronomy, 1886. The Stars, 1902. 
Young, General Astronomy, 1904. 
Langley, The New Astronomy, 1 894. 
See, T. J. J., Evolution of the Stellar Systems, 1896. 
Faye, Sur TOrigine du Monde, 1896. 
Lockyer, J. N., Meteoritic Hypothesis, 1890. 
Thomson, J. J., Conduction of Electricity in Gases, 1903. Electricity 

and Matter, 1904. 
Vogel- Newcomb, Populare Astronomic, dritte Aufi., 1905. 
Baur, Chemische Kosmographie, 1903. 
Righi, La Moderna Teoria dei Fenomeni Fisici, 1904. 



INDEX 



INDEX 



Abacus, calculating machine, 58 
Abdera, Greek city in Thrake, 131 
Aberration of the stars, Bradley's 

discovery of, 286 
Abjuration of Galileo, 196 
Absorption of light, 395 
Academy, French, its expedition 

to Cayenne, 230 
Acceleration of falling bodies known 

to the ancients, 124 
Acceleration of falling bodies first 

measured by Galileo, 198 
Accuracy, extraordinary, of modern 

observations, 232 
Acoustics, studied by the Greeks, 

147 
Action at a distance, inconceivable, 

449 
Adams, J. C., predicts an extra- 

Uranian planet, 311 
Africa, circumnavigation of, 80, 

160 
Ahmes, manuscript of, 56 
d'Ailly, his Imago Mundi, 10 

transmits Roger Bacon's ideas, 

160 
Air, ancient ideas of materiality of, 

138 
weight of, demonstrated by Tor- 

ricelli, 240 
pump, invented by Guericke, 241 

Akosmism, Fichte's, as an alter- 
native, 9 

Alchemy, beginnings of, 51 

d'Alembert, French mathematician, 
296 

Alexandria, its stirring life, 80 
its decline, 146 

Alexandrian school, its long sur- 
vival, 126 

Algebra, early use of, 58 

Al-Hassan, founder of the Assassins, 

155 
Al-Hazen calculates the height of 
the earth's atmosphere, 241 

473 



Almagest, Ptolemy's, Coppernicus' 
debt to, 164 

Al-Maimum, measure of the earth, 
78 
collects a great library, 153 

Alpha Centauri, size of, 336 
a double star, 2,7Z 
distance from the earth, 357 

Alphonso of Castile, his remark, 17 

Amber, first manifests electrical 
properties, 139 

America, discovery of, its effect on 
Europe, 163 ' 

Anaxagoras, ideas of the sun, 22 
ideas of attraction, 123 
on homeomericB or similar parts, 
136 

Andalusia, public libraries in, 154 

Anderson, observation of new star, 
380 

Antony, Mark, presents a library to 
Cleopatra, 152 

Apelt, his history of ideas, 10 

Apex, stellar, the direction of sun's 
movement, 323 

ApoUonius of Perga, introduced 
conic sections, 92 
on Mercury and Venus as satel- 
lites of the sun, 169 

Appearances, difficulty of over- 
coming, 21 

Apple, Newton's, probably a myth, 

257 
Arabian culture, its character, 156 
Arcetri, death-place of Galileo, 207 
Archimedes, inscription on his 
tomb, 57 
description of his planetarium — 
failure to adopt Aristarchus' 
ideas, 116 
his "Arenarius" or sand-reck- 
oner, III 
his greatness and limitations, 125 
Arcturus, vast size of, 337 
its frightful speed, 340 



474 



INDEX 



Arcturus, its unaccountable speed, 

447 
" Arenarius," a work of Archi- 
medes, III 
Aristarchus, of Alexandria, on 
motion of the earth, 22 
anticipation of the Coppernican 

idea, 112 
measures distance of the sun, 89 
on distance of the sun, 93 
on the path of the moon, 169 
Aristotle, on spontaneous genera- 
tion, 5 
copies much from Democritus, 

134 
his doctrine of a fixed earth, 

102 
Middle Age deification of, 156 
on size of the earth, 75 
Armils, accuracy of Alexandrian, 

95 
Arnold, Sir Edwin, his poem, 155 
Arnold, Matthew, quoted, 2, 370 
Arrhenius, work on cosmical physics, 
12 
ideas of cosmogony, 423 
on origin of meteorites, 437 
on the cycle of matter, 461 
Assassins, Al-Hassan, founder of 

sect, 155 
Asteroids, discovery of, 307 
Astronomical knowledge, synonym 

of certitude, ny 
Atheism, periods of its recurrence, 

159 
Atheists, the first of, 141 
Athens, lateness of its intellectual 

awakening, 131 
Atmosphere, height of the earth's, 

241 
Atomic idea, early arguments for, 

136 
Atoms, early ideas of, 136 

rain of, in space, Democritus' 
conception of, 138 
Attraction, early ideas of, 122 
Coppernicus on, 170 
Gilbert's ideas of, 190 
insufficient to hold the stars in 

a system, 446 
Kepler on, 188 
law of, Newton's account of its 

discovery, 255 
Newton's discovery rejected by 

Huyghens, 246 
true nature of Newton's dis- 
covery, 260 
Augustine, St., his age, 151 | 



Auzout, applies the micrometer to 

telescopes, 245 
Averroes, his type of thought, 156 
mistaken observation of Mercury, 

221 
Avicenna, his type of thought, 156 

Bacilli, structure and size of, 40 
Bacon, Lord, quotation from Plato, 

99 
apology for, 203 
estimate of his work, 213 
ideas on attraction, 246 
ignorant of Kepler's work, 192 
on Coppernicus, 212 
on Democritus, 130 
rejection of Coppernican theory, 
177 
Bacon, Roger, influence on Colum- 
bus, 159 
describes the telescope, 200 
Bacteria, obscure utility of, 16 
Baer, von, stimulus to Spencer, 136 
Bailly, his History of Astronomy, 11 
on early measures of the earth, "jy 
on the parallax of the sun, 95 
quotation from, on astronomy, 1 10 
quotation from, 268 
Balance, the, discovery of, 54 
Bankruptcy of science, 39 
Barometer, discovered by Torri- 

celli, 240 
Bel, servitors of, 68 
Benn, on early mathematics, 57 
Bentley, Newton's letter to, on 

gravitation, 452 
Berenson, method of identifying 

painters, 380 
Berkeley, Bishop, conceptions of a 

dream world, 31 
Bernouillis, the, family of mathe- 
maticians, 295 
calculus of the solar system, 402 
Bessel, the first to determine stellar 
parallax, 334 
on astronomy of the invisible, 372 
Bethlehem, Star of, 379 
Binary systems, Herschel's dis- 
covery of, 324 
probable origin of, 378 
spectroscopic, 374 
Binomial theorem, invented by 

Newton, 255 
Bion, his teachings, 64 
Bjerknes, hydro-mechanical theory 

of gravitation, 455 
Boccaccio, an evangel of the Re- 
naissance, 159 



INDEX 



475 



Bode, law of spacing of the planets, 

307 
Body, human, regarded as a 

machine, 32 
Boileau, Bishop, resists the effort 

to suppress new ideas, 220 
du Bois-Reymond, quotation from, 

253 
Books, price of, in ancient times, 

175 
Borelli, ideas on gravitation, 246 
Bouguer, invention of the helio- 

meter, 3 33 
Bouillaud, ideas on gravitation, 246 
Boyle, and Harriot, on laws of 

pneumatics, 242 
likens universe to Strasburg 

clock, 247 
Newton's letter to, on gravi- 
tation, 450 
Bradley, discovers the aberration 

of the stars, 286 
discovers nutation, 288 
on movement of the solar 

system, 321 
Brahma, hatching out the universe, 

401 
Brewster, Sir David, on Lord 

Bacon, 214 
account of Newton's discoveries, 

257 
Brightness of the stars, measure of 

relative distance, 390 
Browning quoted, 2 
Bruno, on plurality of worlds, 30 

his life and ideas, 177 
Buckle, History of Civilisation, 1 1 
Buffon, his good gorilla, 49 

on origin of the solar system, 402 
Burning glass, very old, 200 

C^SAR, his huge debts, 149 

death of, visited by heavenly 
portents, 269 
Calculating spirit, its temperature, 

87 
Camera, used in photographing 

spectra, 348 
Campo di Fiori, Bruno burned in, 

180 
Canopus, its probable distance and 
grandeur, 337 
evidences increasing congrega- 
tion of matter, 459 
lower limit of distance, 360 
reflections on a planet as large as, 
36s 
Carlyle, quotation from, 316 



Carnot, founds thermo-dynamics, 

415 
Cassini, fixes the true distance of 

the sun, 229 
Cause, Hume on idea of, 462 
Cayenne, results of the expedition 

to, 230 
Celestial mechanics, founded by 

Newton, 260 
Celoria, distribution of the stars, 

393 
Cena de le Ceneri, La, a work by 

Bruno, 179 
Central sun, Lambert's idea of, 388 
Centre of solar system, earth as, 

104 
Ceres, discovery of, 308 
Certitude, beginnings of, 49 
Chaldeans, their measure of the 

earth, 75 
Chance, Democritus' conceptions of, 

141 
solar system not due to, 402 
Charles II., his reign the golden age 

of English science, 263 
Charles the Hammer — check of the 

Saracen, 157 
Charles the Wise founds Royal 

Library of France, 152 
Charron, the sceptic, Gassendi's re- 
semblance to, 221 
Chatelet, Madame du, translates 

Newton's Principia, 265 
Cheerfulness, Democritus' idea of 

the highest good, 142 
Cheops, orientation of his tomb, 

lOI 

its geometrical construction, 68 
Chinese, slight value of their con- 
tributions, 157 
Chronometer, perfected by Harri- 
son, 244 
Cicero, his Commonwealth, 116 
Academics, quoted, 354 
belief in divination, 269 
on gravitation, 121 
on the value of life, 147 
testimony to Democritus* style, 
132 
Circle, divisions of, 54 
Civilisation, its former precarious- 
ness, 14 
revelations of its antiquity, 25 
ancient, its frail foundation, 127 
Clairaut, mathematical investiga- 
tions, 295 
Clark, discovery of Sirius* com- 
panion, 372 



476 



INDEX 



Cleomedes, on measure of the sun, 

94 
failure to accept Aristarchus' 

ideas, ii6 
proof of littleness of the earth, 

112 

Gierke, number of new stars, 379 
Clocks, invention of, 243 
Cogito ergo sum, keynote of Des- 
cartes' philosophy, 218 
Colding, discovery of conservation 

of energy, 416 
Collision of suns is incessant, 378 

of nebulae and suns, 421 
Colonies, Greek, 102 
Columbus, his great project, 160 

effect of his discoveries, 163 
Gometary origin of the planets, 

Bufion's idea of, 404 
Comets, the terror they once in- 
spired — orbit of, first calculated 
by Newton, 270 
tails, their enormous length, 273 
their disintegration into meteor- 
itic swarms, 276 
Compass, introduction of, 158 
Gomstock, on absorption of light, 

395 

Congregation of the Index, judg- 
ment against Galileo, 196 

Conical shadow of the earth, its 
implications, 91 

Conservation of energy, establish- 
ment of the idea of, 416 

Constantinople, the fall of, 158 

Constellations, fanciful names of, 

99 
Constructive impulse, 18 
Coppernican theory, iii justice of 
the name, 114 
its truth demonstrated by 

Galileo, 202 
not put forward as a hypothesis, 

166 
system, perfected by Kepler, 191 
Coppernicus, quotation from, vii, 
162 
his argument against the revolu- 
tion of the fixed stars, 102 
his life and ideas, 164 
proof of littleness of the earth, 
112 
Coral polyps, the changes they have 

wrought, 464 
Cordova, Saracen capital, 154 
Corpuscles, rain of, from candescent 
bodies, 433 
enormous speed of, 434 



Correlation of forces, a nineteenth- 
century discovery, 416 
Cosmic structure, Struve and 
Proctor on, 391 
dust, Arrhenius on, 395 
exchange, the, of matter and life, 
429 
Cosmological letters, Lambert's, 387 
Cosmos, likened to a gas, 397 

eternity of, 424 
Cosmotheoros, a work by Huyghens, 

245 
Crassus, source of his wealth, 149 
Creation, the increasing mystery 
of, 398 
primitive ideas of, 401 
Critical diameter of minute par- 
ticles, 434 
Crito, speech to Socrates, 458 
Croll, on stellar collisions, 452 
Crusaders burn the Tripoli Library, 

154 
Curve of development, 36 
Cycle of matter, Arrhenius on, 

461 
Cyril, Saint, the murder of Hypatia, 

153 

Dalton, John, founder of modern 

chemistry, 128 
Dante, creates Italian poetry, 159 
quotation from II Paradiso, 304 
Dark stars, Stoney on number of, 

382 
Darwin, age of discovery of natural 

selection, 406 
Decimal system, Hindu origin of, 

58 
Deer, methods of reasoning in, 9 
Democritus, of Abdera, inscription 
to, V 
his Diakosmos, 10 
his doctrines, 15 
his life and ideas, 131 
Deneb, its enormous size, 338 
Density of the sun and planets, 
Buffon's calculation, 404 
of star spacing, 430 
Descartes, his life and work, 216 
anticipated by Democritus, 134 
ignorant of Kepler's work, 192 
Kant's paraphrase of, 406 
Design, in the cosmic order, 16 
Diakosmos, chief work of Demo- 
critus, 132 
Dialogues, Galileo's, a brilliant 

work, 205 
Dichotomy of the moon, 89 



INDEX 



477 



Diogenes Laertius, list of Demo- 

critus' works, 132 
Discours de\ la Methode, a work of 

Descartes, 217 
Discoveries, growth of great, 106 
Discovery, era of maritime, 160 
Displacement of stellar spectra, 350 
Dissipation of energy, Kelvin on, 

422 
Distance of the stars, Herschel's 
method of measure, 390 
of the planets accurately deter- 
mined, 232 
DoUond, perfects the heliometer, 

333 

Dominis, Antonio de, his sentence 
and fate, 206 

Double stars, Herschel's observa- 
tion of, 324 
growing knowledge of, 371 

Doubt, Democritus on necessity 
of, 134 

Draper, History of Intellectual De- 
velopment. II 
denunciation of Lord Bacon, 215 

Dust, cosmic, Arrhenius on, 395 

Dynamics, foundations laid by 
Galileo, 198 

Earth, speed of in space, 22 

doctrine of a round, its antiquity 

— when introduced, 64 
its littleness proved by bisection 

of the heavens, 112 
pictured as an animal by 

Kepler, 191 
probable origin, 26 
rate of revolution compared, 317 
shadow of, a cone, 67 
smoothness of, 41 
third motion of, Coppernicus' 
discovery, 167 
Ebert, explains perplexing appear- 
ances in stellar collisions, 381 
Eclipse of the sun and moon, , its 

implications, 91 
Eclipses, early predictions, 64 
Electricity, ancient ignorance of, 

139 

Electro-dynamical theory of gravi- 
tation, 448 

Elements, new, discovered by spec- 
troscope, 348 

Ellipses, Kepler's discovery of 
planetary motion in, 187 

Ellipticity of the earth's orbit 
decreasing, 297 

Emerson, quotations from, 20, 316 



Empedocles, anticipates Darwin, 63 
loves and hates among the 
atoms, 139 
Energy, crudeness of ancient ideas 
of, 139 
of heat, new science of, 415 
supply of from the impact of 
suns, 452 
England, still outside of European 
civilisation in Newton's day, 262 
Ephemerae, Langley's parable on a 

race, 463 
Epicurus, idea of the sun, 5 

borrows his philosophy from 

Democritus, 134 
his rule of life, 218 
inscription over his garden, 155 
life and death of, a work by 

Gassendi, 222 
on chaos, 34 
Epicycles, representation of planet- 
ary motion, 1 1 5 
Eratosthenes, of Alexandria, his 
measure of the earth, 73 
inconsistency of his ideas, 115 
on different levels of the Mediter- 
ranean, 121 
on distance of the sun, 93 
prediction of a new continent, 78 
Erman, Paul, quoted, 344 
Error, ancient limits of, 145 
Ether, suppositions regarding it 

incongruous, 455 
Euclid, permanence of his doc- 
trines, 9 
epigram on mathematics, 57 
his geometry still taught, 146 
his influence on Galileo, 198 
Eudoxus, crystal sphere of the stars, 

106 
Euergetes, Ptolemy, his armils, 95 
Euler, contributions to mathe- 
matics, 295 
Eumenes, collects a vast library, 152 
Evolution, the scheme of, 12 
Bruno's idea on, 182 
idea of, how reached — as a world 

picture, 35 
parallel, of other worlds to our 
own, 363 
Explorers, scientific, as poets, 187 
Exposition du Syst^me du Monde, 
a work by Laplace, 301 

Fall of bodies, Aristotle's ideas. 

198 
Faraday, ideas of matter, 137 
Fatimite Library, at Cairo, 154 



478 



INDEX 



Faust, quotation from, 38 

Ferdinand and Isabella, court of, its 
enlightenment, 63 

Fernel, his measure of the earth, 164 

Fez, Saracen capital, 154 

Figure of the earth, established by- 
Newton, 261 

Finality, impossible in human know- 
ledge, 445 

Fire, discovery of, 50 

First magnitude stars, average 
distance, 360 

FitzGerald, his translations of Omar, 

Fixity in events, difficulty of re- 
cognising, 4 

Fleming, Mrs., discovery of new 
stars, 379 

Fluxions, invented by Newton, 255 

Fontenelle, on the plurality of 
worlds, 233 

Fools, Galileo on number of, 199 

Foot, unit of length, 54 

Force, clarifying conceptions of, 242 
persistence of, Spencer's phrase, 

415 
Forefathers, savagery of our, 14 
Foster, Sir Michael, quotation of, 

144 
Foucault, on wave theory of light, 

346 
Fourth dimension, is improbable, 9 
Foxes, methods of reasoning in, 9 
Fraunhofer, perfects the helio- 
meter, 333 
maps spectrum lines, 346 
Frederick the Great, invites French- 
men to Berlin, 299 
Kant's work dedicated to, 406 
Freedom of the will, its denial by 

Democritus, 141 
Fresnel, wave theory of light, 346 

Galileo, Kepler's tribute to, title 

page 
an early Coppernican, 177 
and Kepler, neither could make 

use of each other's work, 207 
correspondence with Kepler, 199 
estimate of his work, 208 
his abjuration, his life and ideas, 

197 
on distribution of the stars, 281 
on nature's horror of a vacuum, 

240 
on parallax of sun, 95 
to Newton, amazing change of 

ideas from, 326 



Galle, discovers Neptune, 312 
Gascoigne, effect of his inventions, 

95 
invention of micrometer threads, 
244 
Gases, spectrum of, 346 
kinetic theory of, 397 
Gassendi, his life and ideas, 219 
Gauss, his method of least squares, 

308 
General Natural History of the 
Heavens, a work by Kant, 406 
Generation, spontaneous, no evi- 
dence for, 436 
Genius, innateness of, 185 
Geometers, their modes of reason- 
ing, 104 
Geometry, antiquity of, 9 

analytic, developed by Descartes, 

217 
rise of, 56 
Gerber, on rate of propagation of 

gravitation, 453 
Gibbon, -on Omar Khayyam's 

calendar, 155 
Gilbert of Colchester, advocate of 
Coppernican theory, 176 
compared with Lord Bacon, 215 
his ideas on attraction, 190 
Gill, Sir David, on distance of 

Canopus, 360 
Gravitation, first ideas of, 23 

influence on fauna of planets, 365 
investigation of by Royal Society, 

247 
Kant on universality of, 407 
Kepler on, 188 

possible rate of propagation, 453 
relative strength of, 445 
Seeliger on difficulties in law of, 

447 
the riddle of — Newton on diffi- 
culties of conceiving, 449 

Gravity, Coppernicus on, 170 

Greek science, just misses modern 
world conception, 128 

Greeks, the legacy of, 145 

Gregory the Great, mentioned, 152 

Grindstone theory of stellar ar- 
rangement, 387 

Guericke, Otto von, invents the air- 
pump, 241 

Gunpowder, introduction of, 158 

Hall, Maxwell, his system of the 

stars, 396 
Halley, on new method of fixing 

sun's distance, 231 



INDEX 



479 



Halley, discovers changes in the 
position of the stars, 318 
discovers the acceleration of the 

planets, 294 
first prediction of a comet's re- 
turn, 272 
has law of inverse squares, 249 
responsible for Newton's Prin- 
cipia, 253 
Harmonices Mundi, a work by- 
Kepler, 187 
Haroun al-Raschid, his present to 

Charlemagne, 243 
HarpedonaptcB, early surveyors, 56 
Hartley, ideas of mind, 140 
Harvey's discovery of circulation, 

rejected by Bacon, 214 
Heat, memoir by Lavoisier and 
Laplace, 301 
development of new science of, 

415 
of the sun, mystery of, 416 
Heliometer, invention by Savery 

and Bouguer, 333 
Hellenism, a high stage of culture, 

150 
Helmholtz, quotation from, 292 
idea of conservation of energy, 

416 
on extramundane origin of life, 

436 
theory of sun's heat, 417 
Henderson, discovers the parallax 

of the nearest star, 335 
Henri III,, creates a special chair 

for Bruno, 178 
Heraclides of Pontus, his ideas, 102 
Hercules, sun moving towards con- 
stellation of, 323 
Heredity, not evident in the appear- 

f'ance of genius, 293 
Heretics, Europe a holocaust under 

the Inquisition, 164 
I'Hermite, calculates the number of 

the stars, 359 
Hero, or Heron, last of the great 

inventors, 127 
Herschel, Sir John, on the antici- 
pated discovery of Neptune, 
312 
Herschel, Sir William, discovers 
Uranus, 305 
his humble origin — demonstrates 
the movement of the stars, 
318 
ideas on world formation, 414 
method of star gauging, 389 
on the nature of the nebulae, 409 [ 



Herschel, Sir William, penetration 
of his great reflector, 359 

Hicetas of Syracuse, his ideas, 103 
picture of the earth's motion, 106 

Hindus, slight value of their con- 
tributions, 157 

Hipparchus, method of measuring 
the sun, 92 
failure to adopt Aristarchus' 

ideas, 114 
his greatness and his limitations, 
124 

Hippocrates, his visit to Demo- 
critus, 132 

History, the farce of, 12 
its slight present value, 158 

Hobbes, defence of the new doc- 
trines, 222 

d'Holbach, remark to Hume, 298 

HomeomericB, or similar parts, 
Anaxagoras on, 136 

Honian, the bookseller, 155 

Hooke, controversies with Newton, 

259 
devises the escapement for clocks, 

244 
his anticipations of Newton, 247 
Hull and Nichols, demonstrate 

pressure of light, 433 
Humboldt, his Cosmos, 10 

on the force of Galileo's dis- 
coveries, 204 
quotation from his Cosmos, 3 84 
Hume, anticipated by Democritus, 

134 
his dinner with atheists, 298 
on idea of cause, 462 
Huxley, life as molecular mechanics, 

on the value of Greek science, 145 
opinion of Descartes, 216 
Huyghens, perfects the clock, 244 
comparative size of stars, 386 
rejects Newton's discovery of 
attraction, 246 
Hydro-dynamical theories of gravi- 
tation, 455 
Hypatia, the murder of, 153 
Hypothesis, meteoritic, as to sun's 
heat, 417 

Ibn-Junis, application of the pen- 
dulum, 243 

Idealism, Berkeleyan, as an alter- 
native, 9 
its barrenness, 31 

Illusions of sense, Democritus on, 
138 



48o 



INDEX 



Indestructibility of matter, taught 

by Democritus, 1 38 
Index, Coppernicus' work placed on 

the, 171 
India, new route to, 79 
Inferences, validity of scientific, 9 
Infinitude, Lucretius' ideas on, 330 

of worlds, Democritus on, 135 
Inhabitable worlds, enormous num- 
ber of, 362 
Inquisition, its capture of Bruno, 

179 
endeavours to suppress works of 

Coppernicus and Kepler, 192 
its frightful persecutions, 164 
Instauration, Great, quotation from 

Bacon's work, 216 
Interaction of natural forces, a 

lecture by Helmholtz, 418 
Interference, phenomena of, in light, 

346 
Interregnum, accepted picture of, 

151 
Inverse squares, law of, nearly 

reached by Kepler, 190 
Invisible, astronomy of, 371 
Ionian Greeks, their enterprise and 

culture, 131 
Isis, priests of, 68 
Isochronism of the pendulum, 

Galileo's discovery, 198 

Jacobi, on ideas of Anaxagoras, 123 

Joule, establishes the idea of con- 
servation of energy, 416 

Julian Star, carries Caesar to the 
skies, 270 

Jupiter, acceleration of motion, 300 
" Little world " of, presents an 
image of the solar system — 
satellites of, obey Kepler's 
laws, 204 
moons of, discovered by Galileo, 
201 

Kant, on moral sense of man, 39 
criterion of knowledge, 146 
founds the nebular hypothesis, 

405 
on cosmic structure, 387 
on matter, 27 
Kapila, his philosophic views, 9 
Kapteyn, explanation of appear- 
ance of new star spectra, 381 
Keeler, on spiral nebulae, 420 
Kelvin, on age of the sun, 418 
on dissipation of energy, 422 
origin of life, 436 



Kepler, his life and ideas, 185 

computes the distance of the 

sun, 228 
eulogy of Galileo, 209 
his great discoveries ignored, 192 
his rebuke to Rome, 205 
on path of comets, 271 
quoted on Galileo, title page 
Kinetic theory of gases, 397 
Kirchhoflf, discovery of absorption 

spectra, 347 
Kirmess, dance of the stars likened 

to a, 378 
Knowledge, antiquity of, 9 

astronomical, synonym of certi- 
tude, 277 

Lactantius, on globular form of 
earth, 62 
derided by Coppernicus, 169 
Lagrange, his co-operation with 

Laplace, 299 
Lambert, acceleration of Saturn's 
motion, 300 
on structure of the universe, 387 
Lange, history of materialism, 11 

on character of Gassendi, 221 
Langley, illustration of the sun's 
heat, 417 
parable on the end of the world, 

463 
Laplace, on early measures of the 
earth, yj 
eulogy of astronomy, 226 
his life and work, 296 
on Aristarchus, 89 
on astronomy of the invisible, 372 
sketch of the nebular hypothesis, 
410 
Laughing Philosopher, Democritus 

called the, 142 
Lavoisier, anticipations of his ideas 
by Democritus, 138 
memoir on heat, 301 
Law, idea of natural, 4 

scientific, Kepler a pioneer, 188 
Layard, finds a convex lens in 

Nineveh, 200 
Leaning Tower of Pisa used in 

Galileo's experiment, 198 
Lebedeff, demonstrates pressure of 

light, 433 
Lecky, History of Rationalism, 1 1 
Leibnitz, accusations against New- 
ton, 263 
idea of planets as extinct suns, 

402 
invention of the calculus, 295 



INDEX 



481 



Lens, found in palace of Nimrud, 

200 
Leonardo da Vinci, his genius, 159 

not a Coppernican, 177 
Leonids, meteoritic swarm, 276 
Lesage, of Geneva, his theory of 

gravitation, 453 
Lettres Philosophique sur les Anglais, 

Voltaire's, 265 
Leverrier, calculates the orbit of 

the November meteors, 277 
predicts an extra-Uranian planet, 

311 
Leviathan, a work by Hobbes, 223 
Lewes, quotation from his Aris- 
totle, 239 
Libraries, a characteristic of civilisa- 
tion, 152 
Library of Alexandria, its extent, 
III 
Royal, of France, founded, 152 
Life, brevity of human, compared, 
24 
cosmic exchange of, 436 
human, value of, 464 
influence of gravitation on, 366 
physical explanation of, 33 
probable likeness of, throughout 
the universe, 441 
Light, composition of, revealed by 
Newton, 257 
factor of extinction of, 395 
geometry of, 59 
speed of, Bacon's ideas on — 

Roemer's discovery of, 283 
wave theory of, 346 
" Little world, the," of Jupiter 
an image of the solar system, 
204 
Llorente, on victims of the Inquisi- 
tion, 164 
Locke, anticipated by Democritus, 

134 
Logarithms, unknown to the 

Greeks, 146 
Louis XV., his patronage of science, 

230 
Lowell, quotations from his Masac- 

cio, 174, 184 
Lucretius, on the size of the sun, 
22 
on the struggle for existence, 

148 
quotation from his poem, 330 
reports ideas of Democritus, 137 
Luther, his appearance shortly after 
Columbus' discovery, 163 
on the Coppernican theory, 177 



Macaulay, laudation of Lord 

Bacon, 213 
on history, 98 
MacFadyen, experiments on life of 

germs, 439 
Machine, cosmos as a, 465 
Machinery, its wide influence, 150 
Madler, on structure of the Milky 

Way, 392 
Magalhaens, expedition of, 356 
Magnet, The New Physiology of, a 

work by Gilbert, 190 
Magnitudes, stellar, a classification, 

358 
Man, primitive, his ideas of the 

world, 49 
size of, compared with the earth, 

39 
Marco Polo, reports of, 159 
Maria Theresa, remark to Mauper- 

tuis, 234 
Marriot, and Boyle, on pneuma- 
tics, 242 
Martha, translation of Lucretius, 
330 
tribute to Democritus, 135 
Martyrdom, a useless sacrifice, 182 
Mass action, law of, discovered by 
Newton, 259 
of the planets, computed by 

Newton, 261 
of the solar system, 403 
Material of the universe, all the 

same, 348 
Materialism, Democritus as its 
grandsire, 140 
and mechanism, not identical, 
220 
Mathematics, origin of the word, 52 

pay of professors of, 197 
Matter, disintegration of, how far 
it may be carried, 136 
gravitation not an inherent pro- 
perty of, 449 
increasing aggregation of, 459 
indestructibility of, taught by 

Democritus, 138 
new ideas on constitution of, 396 
the unceasing circulation of, 424 
Matterhorn, imaginary being on the, 

85 
Maupertuis, on shape of nebulae, 
405 
reply to Maria Theresa, 234 
Max, Gabriel, portrait of primitive 

man, 49 
Maxwell, Clerk, on pressure of light, 
433 

2 H 



482 



INDEX 



Mayer, discovery of conservation of 
energy, 416 

Measures of the earth, difference in 
early, jy 

Micanique Celeste, a work by La- 
place, 297 

Mechanical appliances, the founda- 
tions of modern knowledge, 331 
contrivances, attributed to black 
art, 415 

Mechanics, effect of new discoveries 
in, 241 
placed on a new footing by 
Galileo, 200 

Mechanism, idea of the world as, 
first consistently expounded by 
Descartes, 219 

Medical schools, first in Europe, 

154 
Mendeleeff, Newtonian scheme of 

molecular constitution, 397 
Mercury, possibly indicates rate of 

propagation of gravitation, 453 
transit of, observed by Gassendi, 

221 
Meredith, George, quotation from, 

444 
Merz, History of Nineteenth-Century 

Thought, II 
Metaphysics, its utter barrenness, 

459 
Meteoric swarms, extra-mundane 

origin of, 432 
Meteorites, origin of, 434 
Meteoritic origin of sun's heat, 416 
swarms, their nature and extent, 

275 
Meteors, identity with comets, 275 
Metrodorus, on plurality of worlds, 

354 
Microbes, conceived as human, 42 
discovery of, 33 

expulsion of, from the atmos- 
phere, 437 
Micro-man, idea of, 40 
Micron, unit of measure, 40 
Middle Ages, reaction in favour of, 

152 
Midnight sun, land of, conjectured, 

147 
Milky Way, Democritus' ideas on, 

135 
ideas on, 386 
structure of, 394 
Milton, quotation from Paradise 
Lost, 280 
visits the blind Galileo, 206 
Mind, decline of the human, 151 



Modern ideas, permanence of, 8 
Moestlin, teaches the Coppernican 

theory, 176 
the teacher of Kepler, 185 
Molecules, spacing of, 430 
Montaigne, writes on the speech of 

the people, 178 
Moon, first measures of distance of, 

87 

Morin, mounted telescope on a bar, 
244 

Mosaic cosmogony destroyed by 
Galileo, 204 

Motes in the sunbeam, suggest idea 
of atoms, 137 

Motion of the earth, absolute de- 
monstration by Bradley, 288 
objections to, 106 

Multiple star systems, 376 

Mystery, the increasing, of creation, 
398 

Mysticism of numbers, Kepler's ad- 
herence to, 186 

Napoleon, reproach to Laplace, 

298 
Nature, religion of, a chimera, 17 

the enigma of, 16 
Nebulae, Herschel's catalogues of, 
325 
origin of, 424 
photography of, its revelations, 

420 
rapid motion of, 441 
worlds in formation in, 30 
Nebular hypothesis, history of, 401 

nuclei, how formed, 421 
Necessity, doctrine of, affirmed by 

Democritus, 142 
Neptune, discovery of, a triumph 
of the law of gravitation, 311 
distance from the earth, 357 
its great distance, 28 
Nero, precedes St. Augustine, 151 
New Astronomy, The, quotation from 

Professor Langley's, 463 
Newcomb, objections to nebular 
hypothesis, 413 
on cosmic structure, 393 
on count of the stars, 359 
on history of nebular hypothesis, 

419 
on Lambert's cosmical theory, 

388 
problem of runaway stars, 445 
New Hypothesis of the Universe, 
a work by Wright of Durham, 



INDEX 



483 



New World, discovery of, a sort of 

laboratory experiment, 160 
Newton, Prof. H. A., discovery of 

nature of meteorites, 275 
Newton, Sir Isaac, character of, 
258 
discoveries, almost anticipated by 

Kepler, 190 
his discoveries and ideas, 253 
his process of discovery, 186 
law of gravitation discovered, 

255 
letters to Bentley, 452 
on atoms, 34 

period of mental eclipse, 263 
New star, Galileo's controversy re- 
garding a, 199 
New stars, spectroscopic detection 

of, 379 
Nicholas of Cusa, observation of 

sun-spots, 181 
Nichols and Hull, demonstrate 

pressure of light, 433 
Nietzsche, Fr., quotation from, viii 

his " blonde beast," 49 
Notations, primitive, 52 
Nova Persei, its distance and 

grandeur, 380 
Novcs, origin of, 380 
Novum Organum, a passage from, 

246 
Nutation, discovered by Bradley, 

288 

Observatory, astronomical, first in 
Europe, 154 

Olbers, finds new asteroids, 309 

Omar Khayyam, his culture and 
character, 155 
myth of burning of the Alexan- 
drian Library, 1 1 1 

Omens, ancient belief in, 4 
belief in, 5 1 

Opinions of Philosophers, a work 
attributed to Plutarch, 93 

Optiks, quotation from Newton's, 

449 
Orbits of stars, 350 

of double stars, 373 
Order, perception of a fixed, 465 
Orders in nature, conjectures on 

their existence, 396 
Oscillatorium Horologium, a work 

by Huyghens, 245 
Osiander, his forged preface to 

Coppernicus, 164 
Ostwald, Wilh., on gravitation, 

453 



Oxford, Bruno's disputations at, 
178 

Pacificus, his early clock, 244 
Paley, his famous work, 263 
Pantheism, Bruno its godfather, 

182 
Papyri, number of, in Alexandrian 

Library, 152 
Parallax, first measurements of, 86 
of the sun, Gahleo's search for, 

202 
of the sun, problem of, 227 
stellar, first discoveries of, 334 
Paris, in the thirteenth century, 

Parliament of Paris, its extra- 
ordinary decree, 220 

Parthenon, golden image in, 69 

Pascal, development of the baro- 
meter, 241 
fright before the infinite, 30 

Pasteur, on spontaneous generation, 
436 

Pattern of worlds, probably not 
very diverse, 364 

Pendulum, isochronism, discovery 
by Galileo, 198 

Pentateuch, the, as a cosmogony, 
10 

Period, of double stars, 374 

Persecution, religious, enormous 
number of its victims, 164 

Petrarch, an evangel of the Re- 
naissance, 159 

Philolaus, of Crotona, his ideas, 
103 

Philosophy, its worthlessness, 15 

Physical sciences, little developed 
among the ancients, 148 

Physics, cosmic, a new study, 

349 

Piazzi, discovery of the first aster- 
oid, 307 

Picard, new measures of the earth, 
256 

Pickering, discovery of spectro- 
scopic binaries, 374 
on distribution of the stars, 

394 
Pivot of the sky, Polaris, loi 
Planet, Kepler's hypothetical, 307 
Planetarium, Archimedes' construc- 
tion of the, 116 
Planetary motion, Kepler's laws of, 
188 
system, shape and arrangement 
of, 314 



484 



INDEX 



Planets, how fertilised with life, 7 
motion of, difficult to map, 385 
motor force of, 208 
orbits of, first correctly arranged 

by Coppernicus, 167 
possible exchange of, 431 
regarded as wandering stars, 27 

Plato, and Aristotle, their credulity, 

.145 
his adherence to a fixed earth, 

102 
inscription on his Academy, 57 
on numbers, 52 
on the Greeks, 98 
quotation from his Crito, 458 
wished to burn works of Demo- 
critus, 134 
Pliny, his Natural History, 10 
on weather forecasting, 149 
story of Democritus' power to 
raise the dead, 132 
Plurality des Mondes, a work by 

Fontenelle, 386 
Plurality of worlds, taught by 

Bruno, 180 
Plutarch, on cessation of rotary 

force, 123 
Plutocracy, always a dominant 

power, 149 
Polaris, a double star, 375 
Polemic, Gassendi as a model of, 

222 
Pole Star, distance from the earth, 

357 

Pons asinorum of intellectual de- 
velopment, 5 

Pope, his epigram on Newton, 
264 

Populace, the mind of, 150 

Porta, Delia, on force of steam, 

243 

Poseidonius, failure to accept Aris- 
tarchus' ideas, 116 
measure of the earth, 76 
on distance and diameter of the 

sun and moon, 94 
on the tides, 122 

Precession of the equinoxes, cause 
of, 167 

Preston, S. Tolver, on Lesage's 
theory of gravitation, 454 

Prevost, fixes direction of the sun's 
motion, 322 

Priesthood, Egyptian, their learn- 
ing. 56 

Principia, Newton's, generally re- 
jected by his contemporaries, 
265 



Principia, of Descartes, its profound 
influence, 239 
of Newton, its origin and con- 
tents, 253 
quotations from Newton's, 449 
Printing-press, effect of its intro- 
duction, 175 
Proctor, on cosmic structure, 391 
Procyon, companion sun of, 372 
Proportion, development of idea of, 

55 
Protagoras, first of the atheists, 

141 
Protyl, 34 

Psalm, quotation from 52nd, 400 
Ptolemaic system, Schiaparelli on, 

165 
Ptolemies, court of, no Columbus 

at, 80 
found the Alexandrian Library, 

152 
the, Greek kings, 57 
Ptolemy, C, measure of the earth, 

79 
on measure of the sun, 92 
on parallax of the moon, 87 
Publishing, rapid growth of, in the 

fifteenth century, 175 
Pulsilogy, an invention of Galileo's, 

198 
Pyramids, how measured, 55 
Pythagoras, sacrifices a hecatomb 

in honour of his discovery, 

57 
taught revolution of the earth, 

102 

Queries, quotation from one of 

Newton's, 451 

Ramsay, Sir William, on formation 
of matter, 435 

Ranke, estimate of the number of 
victims of religious persecu- 
tion, 164 

Rationalism, its slight influence, 
150 

Reflecting telescope, invented by 
Newton, 257 

Reformation, early attempts before 
Luther, 176 
follows discovery of America, 163 
the, might have been anticipated, 

157 
Refraction, Ptolemy on, 200 
Religion in the Middle Ages, 156 
rational, first taught by Bruno, 



INDEX 



485 



Renaissance, the problem of, 158 
Renan, on curiosity, 5 

quotation from Dialogues Philoso- 

phiques, 212 
Revelation, quotation from Book 

of, 48 
Revolution of the earth, difficulty 

of conceiving, 103 
Revolutionihus, De, Coppernicus' 

work, analysed, 164 
Rheticus, disciple of Coppernicus, 

176 
Richelieu, Cardinal, procures an 

extraordinary decree from the 

Parliament at Paris, 220 
Riehl, on Bruno, 181 
Rigel, its enormous size, 338 
Roemer, discovers the speed of 

light, 284 
Roman civilisation, exhaustion of, 

151 
Rome, its age of culture, 146 
Rosenberger, account of Newton's 

discoveries, 257 
Rosse, Lord, observations on spiral 

nebulae, 420 
Rotation of the sun affirmed by 

Bruno, 181 
Royal Society, its origin, 247 
Rubens, his picture in the Louvre, 

378 
Rumford, on nature of heat, 41 5 
"Run-away" star, 1830 Groom- 
bridge, 340 
stars, Newcomb's problem of, 

446 

Sakya-Muni, mentioned, 155 
Salons, French, patronised by men 

of science, 233 
Samarcand, Saracen capital, 154 
Sanctorius, invention of a pendu- 
lum clock, 244 
Saracens, their great libraries, 153 
Saturn's rings, a picture of world 
formation, 408 
demonstrated by Huyghens, 245 
Savery, invention of the heliometer, 

333 

Scepticism, need of scientific, 462 

Schiaparelli, on Ptolemaic and 
Coppernican systems, 165 
on theory of epicycles, 115 

Schonberg, Cardinal, letter to Cop- 
pernicus, 176 

Science, ancient, sparseness of dis- 
covery in, 127 
civilisation as the work of, 6 



Science, value of Greek, 146 

Sea, general level of, 121 

Sebastian d'Elcano, first circum- 
navigation of the earth, 356 

See, T. J. J., Evolution of Stellar 
Systems, 431 

Seeliger, on distribution of the 
stars, 393 
on the infinity of the universe, 

447 
Seleucus of Babylon, follower of 

Aristarchus, 114 
Seneca, inscription in Epicurus' 

garden, 155 
Sensation, Democritus' ideas on, 

134 
Serapis, library in the temple of, 

152 
Sexagesimal system, 53 
Shakespeare, appropriates Bruno's 

comedies, 178 
Shattered planet, theory of, 309 
Shelley, his Hellas quoted, 428 
Shooting-stars, degenerated comets, 

275 
Simplicius, ideas of attraction, 1 24 

on grandeur of the stars, 148 
Sirian traveller, viewing the earth, 

44 
Sirius, distance from the earth, 

357 

its dark companion, 372 

size of, T,T,7 
Sizzi, on Galileo's discoveries, 203 
Skies, fascination of Mediterranean, 

99 
Slavery, in ancient society, 50 

in England, lateness of, 14 
Slaves, first men of science, 51 
Socrates, contempt of astronomy, 

135 
idea of the earth, 5 
speech of Crito to, 458 
Solar history, stages of, 424 
Solar system, dimensions of the, 
30s 
ideas on origin of, 402 
motion of, 318 
stability of, 446 
Solomon, believed in a flat earth, 5 
Somerset, Lord, his early steam- 
engine, 243 
Somnium Astronomicum, a work 

by Kepler, 245 
Sorbonne, Bruno's letter to the, 

179 
Space, demonstration that it is 
practically empty, 242 



486 



INDEX 



Space, not so empty as was sup- 
posed, 395 

Spacing of the planets, Bode's law, 
306 

Spectroscope, revelations of, 345 

Spectroscopic binaries, discovery of, 

374 
Spectrum, named by Newton, 345 
Speed of the sun's translatory 

motion, 323 
Spencer, his doctrine compared to 
that of Democritus, 140 
on registered experience, 9 
value of his philosophy, 15 
Sphericity of the earth, early argu- 
ments for, 6s 
Spinoza, Bruno his godfather, 

182 
Spiral nebulae. Lord Rosse's ob- 
servations, 420 
Spores, size and nature of, 437 
Stability, of binary systems, 377 

of the solar system, 293, 446 
Stadia, varying lengths of, ^y 
Stadium, unit of distance, 54 
Star gauging, Herschel's method of, 

389 
history, three stages of, 424 
light, I'Hermite's calculation of, 

361 
streams. Proctor on, 392 
Starry universe, extent of, 361 
Stars, average distance of first 
magnitude, 360 
nearest, their distance, 29 
outside limit of number, 359 
radial velocity of, 349 
spectrum characteristics of, 349 
speed of the, 340 
Stellar system, possible loss of stars 

from, 447 
Stoney, on number of dark stars, 

382 
Strabo, prediction of a new con- 
tinent, 78 
ridicules Eratosthenes' ideas — his 
notions of gravity, 121 
Structure of the heavens, a work by 
Herschel, 406 
of the universe, theories of, 

385 
Struve, on cosmic structure, 391 

parallax of Vega, 335 
Sun, absolute distance of, 231 
age of, 418 
calculations as to visual diameter 

of, 147 
comparative grandeur of, 337 



Sun, evidently distant and large, 67 
first measure of its distance, 89 
fixity of, first imagined, 104 
its position in space, 362 
its shifting position, 65 
Kepler likens to a great magnet, 

190 
mediocrity of our, 339 
movement of translation, 320 
origin of its heat, 416 
spectrum of, 347 
volume of the, 234 
Sunlight, pressure of, 433 

rays of, parallel, 59 
Suns, collision of, is incessant, 

378 
Sun's motion in space, path of the, 

323 
Sun-spots, Galileo's demonstration 

of, 204 
Super-men, Democritus' idea of, 

141 
Swift, fanciful tale, 40 
System of the universe, Lambert's, 

387 
solar, how it would look from the 
outside, 27 

Taine, on English slaves, 12 
on truth, 188 

Telescope, first described by Roger 
Bacon — history of its discovery, 
200 
penetration of Herschel's great 
reflecting, 359 

Telescopes, colossal, of Auzout and 
others — accuracy of modern, 
281 

Tennyson, quotation from In Memo- 
Ham, 25, 428 

Tetrad, grand, 52 

Thales, measure of the Great Pyra- 
mid, 55 
quotations from, 84 

Theophilus, Bishop, destroys Alex- 
andrian Library, 153 

Theory of the Earth, a work by 
Bufion, 402 

Thermo-dynamics, founded by Car- 
not, 415 

Thermoscope, Galileo's invention, 

243 
Thompson, Benjamin {see Count 

Rumford), 415 
Thomson, J. J., on constitution of 

matter, 396 
Thomson, Sir Wm. {see Lord 

Kelvin), 418 



INDEX 



487 



Three bodies, problem of, 296 
Tides, early observations of, 123 
Kepler on, 189 
Galileo on, 189 
theory of, established by Newton, 

262 
Time, ancient lack of an accurate 

measure of, 126 
Torquemada, the number of his 

victims, 164 
Torricelli, discovery of the baro- 
meter, 240 
Toscanelli, encourages Columbus, 

160 
ideas of, 79 
Tourbillons, or vortices, imagined 

by Descartes, 219 
Trigonometry, its late development, 

146 
Triple star systems, 376 
Tripoli, its library burnt, 154 
Twentieth century, attains to a 

true cosmic picture, 7 
Tycho Brahe, famous star of, 

379 

his observations utilised by Kep- 
ler, 186 

objections to Coppernican idea, 
28 

on origin of comets, 271 
Tyndall, his conception of material- 
ism, 140 

littleness and greatness of man, 

39 
Types of stellar arrangement, 376 



Ulptan library, in Rome, 153 
Uniformity, remarkable, of planet- 
ary motions, 403 
Universe, as a flower garden, 
Herschel's idea of, 410 
as a cyclic process, 7 
binding force of, 445 
end of, 459 
extent of, Coppernicus' ideas of, 

166 
Newcomb on limits of, 359 
pictured as a gas, 429 
Unthinkables, Democritus' choice 

of, 137 
Uranus, discovered by Herschel, 

30s 
Urban VIII., inscription on his 

brother's tomb, 159 
Urstoff, 34 
Usher, Archbishop, date of creation, 

24 



Vacuum, limits of, obtainable, 429 

nature's horror of, 240 
Vanini, torture and fate, 206 
Vaucanson, marvels of mechanics, 

415 
Vendelinus, estimate of the distance 

of the sun, 229 
Venus, distance from the earth, 

356 
phases of, discovered by Galileo, 

202 
transit of, first observed by 

Horrox, 222 
Velocity, surface, of the earth, 317 
Vinci, See Leonardo da Vinci 
Virgil, quoted, 105 
Virginia Reel, cosmos likened to a, 

431 

Vives, Ludovicus, quotation, 72 

Viviani, carries out Torricelli's ex- 
periment, 240 

Vogel, discovery of spectroscopic 
binaries, 374 

Voltaire, a sincere deist, 298 
his ironical inquiry, 435 
introduces Newton to France, 

264 
tale of Micvomegas, 44 

Vortex ring theory, 219 

Vortices, the foundation of Des- 
cartes' system, 219 

Voyages, extent of ancient, 355 



Wallis, his treatise on gravity, 

254 
Washington, George, mentioned, 

149 
Weather predictions of Democritus, 

13s 

Wheel, bacillus on the, 39 

Whewell, his History of Science, 10 

Williams, on methods of animal 
reasoning, 9 

Wittenberg, the Athens of Ger- 
many, 179 

Wollaston, maps, spectrum lines, 
346 

Wordsworth, his " Mutability " 
quoted, 400 

World formation, a mechanical 
process, 7 
image, difficulty of constructing 
a, 3 

Worlds, the birth and death of, 
401 

Wren, Sir Christopher, law of in- 
verse squares, 298 



488 



INDEX 



Wright of Durham, author of the 
Grindstone Theory, 386 

Xerxes, entertained at Abdera, 131 
Ximenes, Cardinal, destroys valu- 
able manuscripts, 154 

Year, early measures of, 53 
Young, Dr. Thomas, on interfer- 
ence, 346 



Young, Prof. C. A., on strength of 
gravitation, 445 

Zenophanes, early ideas of geology, 

148 
Zero, introduction of, 58 
Zodiac, circle of the animals, 104 
Zone of no shadow around Syene, 

59 
Zones, first conceptions of, lOi 



THE END 



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